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User: 25631 Logic gatesINTRODUCTION Logic gates are electronic components used in registers, memory chips and pro cessors to evaluate Boolean expressions . Therefore, before you read  this chapter, you must understand the basic Boolean expressions described in the previous chapter. This is because there is a one-to-one relationship between Boolean expressions and logic gates. Logic gates are represented as logic diagrams and also have a corresponding truth table. Consequently there is a logic diagram for each of the main Boolean expressions that we have looked at in the previous chapter. LEARNING OBJECTIVES In this chapter you will learn: •that there is a one-to-one relationship between logic gates andBoolean expressions •how logic gates are combined to build circuits within processors•how logic gates are used to evaluate Boolean expressions to producea result •how logic gates can be combined to create full systems •what full and half adders are.
 A-level students will learn: •what an edge-triggered D-type ﬂ  ip-ﬂ op  is.SPECIFICATION COVERAGE 3.6.4 Logic gates3.6.5 Boolean algebra KEYWORDSLogic gate: an electronic component used to perform Boolean algorithms.
 Boolean expressions: an equation  made up of Boolean operations.257The logic gates for each of the six basic Boolean expressions are shown in Figure 31.1.
 Gate Symbol OperatorA+B AAsB AsB A+Bandornot nandnor xor A + B Figure 31.1 Logic gate symbols and corresponding Boolean expressionsLogic gates take inputs and produce a single output. In the electronic circuit, the inputs are voltages with a high voltage representing a 1 and a low voltage representing a 0. For example, the logic gate for an AND expression is shown below: A B 2-input AND GateQFigure 31.2 The AND gateA and B are the inputs and Q is the output so this diagram is the equivalent of A.B = Q The standard ANSI/IEEE standard 91-1984 diagram for each logic gate is shown below along with its truth table and Boolean notation for ease of reference.
 SymbolBoolean expression Q = A.B A AND B = QTruth tableA     B          Q 0     0          00     1           01     0          01     1          1 AB 2-input AND GateQ Figure 31.3 The AND gate with truth tableKEYWORDAND gate: result is true if both inputsare true.31 LOGIC GATES258  31 Logic gatesSymbolBoolean expression Q = A+B A OR B = QTruth tableA     B          Q 0     0          00     1           11     0          11     1          1 AB 2-input OR GateQ Figure 31.4 The OR gate with truth tableSymbol Boolean expression Q = NOT A or A The inversion of A = QTruth tableA Q0 1 1 0A Inverter or NOT GateQFigure 31.5 The NOT gate with truth table SymbolBoolean expression Q = A.B A AND B = NOT QTruth tableA     B          Q0     0          10     1           11     0          11     1          0 AB 2-input NAND GateQ Figure 31.6 The NAND gate with truth tableSymbol Boolean expression Q = A+B A OR B = NOT QTruth tableA     B          Q0     0          10     1           01     0          01     1          0A B 2-input NOR GateQFigure 31.7 The NOR gate with truth tableKEYWORD NAND gate: result is true if any of the inputs are false.KEYWORD OR gate: result is true if either  input is true.
 KEYWORDNOT gate: inverts the result so true becomes false and false becomes true.
 KEYWORDNOR gate: result is true if both inputsare false.COMBINING LOGIC GATES 259SymbolBoolean expression Q = A + BTruth tableA     B          Q 0     0          00     1           11     0          11     1          0 AB 2-input Ex-OR GateQ Figure 31.8 The XOR gate with truth table●Combining logic gates Logic circuits are made up of a series of logic gates to create full systems.
 These can get very complex as there may be thousands of gates connected together. The output from the first gate becomes the input for the secondgate and so on. Therefore there will be various values generated until a finalvalue of Q is arrived at.
 For example, Figure 31.9 shows a simple alarm system where A and B areinputs from sensors and C is the manual override to turn the alarm off.O A or B = 1 means that the sensors have picked up an intruder. O A or B = 0 means that the sensors have not picked up an intruder.
 O C = 1 means that the override button has been pressed to turn the alarm off.O C = 0 means that the alarm will continue to sound.
 Therefore the only scenario where the alarm would sound is if either A ORB = 1 AND C = 0, which could be written as (A+B).C This could be shown as Q = (A+B).C and represented in the logic diagramin Figure 31.9 with the corresponding truth table.
 A+B AB C(A+B) sCC InputsA           B           C        Q 0           0           0        00           0           1        0 0           1   0        10           1           1        0 1           0           0        11           0           1        0 1           1           0        11           1                   1        0Outputs Figure 31.9 A logic circuit with truth tableKEYWORD Logic circuit: a combination of logic gates.KEYWORD XOR gate: result is true if either input is true but not if both  inputs are true.26031 Logic gatesTo follow this through: O Inputs from A and B pass through an OR gate. O Input C passes through a NOT gate. O These two results are passed through an AND gate to create the final result.In the example above a logic circuit has been constructed from the Boolean expression. It is also possible to construct a Boolean expression from a logic circuit. For example: C+DABC D(AsB)s(C+D)AsBAs the logic circuits get more complex, so the corresponding Boolean expression will get more complex: A B CAsBA+(AsB)+CA+(AsB)A●Full and half adderTo add together binary numbers, electronic circuits called adders are used.These are formed by combining logic gates together. Adders are commonlyfound in the Arithmetic Logic Unit (ALU)  in the CPU. There are two main t ypes, the half adder  and the full adder . To understand thisecti on, you need to make sure you have read Chapter 24 on adding binarynumbers together. Adders take in two bits A and B and add them to create a sum, S. So A + B = S.
 There is a further bit required called a carry bit , for when the result of the sumrequires a further digit. For example, binary addition of 1 + 1 results in 10 (i.e. 0 carry 1), so the carry bit is needed to store this additional bit.A half adder calculates the sum and stores the value of the carry bit C as well as the result S. The logic diagram to represent this is shown in Figure 31.10.
 AS CB Figure 31.10 A logic circuit for a half adderKEYWORDSArithmetic Logic Unit (ALU): partof the processor that processes and manipulates data.
 Half adder: a circuit that perf orms addition using inputs from A and B only.Full adder: a circuit that perf orms addition using inputs from A and B plus a carry bit.Carry bit: used to store a 0 or 1 dependin g on the result of binary addition.FULL AND HALF ADDER 261The XOR gate is used to look at inputs A and B: O If A = 0 and B = 1 or if A = 1 and B = 0 then the value for S will be 1. O Where A and B are both 0, the sum will be 0. O Where A and B are both 1, then the answer is 10 in binary, which means  that 0 is the result for S with the 1 put into the carry bit.
 The truth table shows the values of C and S for every possible input of A and B.
 Inputs OutputsABCS 0000100101011110 Half adders can be added/chained together to create a full adder. Full adders take three inputs, which are the two binary digits to be added, plus the carry bit from the previous addition. The output is the sum (S) plus the carry bit. Notice in the logic diagram below that Cin represents the value of the carry bit at the start of the addition and C out is the value of the carry bit at the end. C out from the first addition becomes C in on the second addition and so on.A Cin CoutB SFigure 31.11 A logic circuit for a full adderO The XOR gate works in the same way as a half adder to identify where the values of A and B are different. Where they are different the result is 1; where they are the same the result is 0.O A second XOR gate is used to perform the same function on the result of A and B with the value of C in to generate S. O A and B are ANDed together. O Cin is ANDed with the result A XOR B.
 O These two are ORed together to calculate C out.
 The truth table shows the values of C in and C out and S for every possible input of A and B. Inputs OutputsAB C in Cout S 00 0 0 010 0 0 1 010 0 1 11 0 1 00 1 0 110 1 1 001 1 1 011 1 1 1262 31 Logic gates●Edge-triggered D-type flip-flop Logic gates and logic circuits show how 0s and 1s can be manipulated to evaluate Boolean expressions. Data is passed around these gates and circuits at very high speed. However, as soon as the next set of inputs are fed in, the previous inputs are lost. As we have seen, often the next set of inputs come from the outputs of the previous calculation. Therefore some form of memory is needed and this is provided by a flip-flop , which is capable of storing one bit. Logic circuitMemory unitPrimary outputsSecondary outputsPrimaryinputs Secondaryinputs Figure 31.12 An edge-triggered D-type ﬂip-ﬂopThis means that the logic circuit is now receiving two sets of inputs, primary and secondary. It uses the system clock  to synchronise these requests. Each pulse of the system clock has a rising edge and a falling edge, which represents each pulse of the clock. Figure 31.13 How the ‘edge’ triggers a change of stateA level onlyKEYWORDS Flip-flop: a memory unit that can st ore one bit.
 Edge-triggered D-type flip-flop: a memory unit that changes state with each pulse of the clock.
 Clock: a device that generates a signal used to synchronise the components of a computer. Clock periodClock width Rising edgeFalling edgeIn the case of an edge-triggered D-type flip-flop this means that on each pulse of the clock, the flip-flop will change state. This means that for each pulse of the clock, data coming from the input will be stored in the flip-flop and continue to be output until the next trigger pulse is received.
 Practice questions can be found at the end of the section on page 264.
 EDGE-TRIGGERED D-TYPE FLIP-FLOP 263STUDY / RESEARCH TASKS1 Create a full speciﬁcation for an embedded system, e.g. operation of a  lift or an alarm system, implemented in the form of logic diagrams.2 Research SR, T and JK ﬂip-ﬂops. Find out how they work. 3 Explore how NAND gates can be used to create memory chips.KEY POINTS •Logic gates are a way of designing and describing the way in which electroniccomponents within registersand processor are constructed.
 •Logic gates evaluate Booleanexpresions. •There are six main symbolsthat relate directly to the six main Boolean expressions.
 •Logic gates can be combinedto represent more complex systems.
 •Logic gates effectivelyshow 0s and 1s are manipulated and binaryaddition takes place withinthem using either a half or fulladder.
 •An edge-triggered D-typeﬂip-ﬂop is a memory unit that temporarily stores the resultof an operation.TASKS1 What is the relationship between Boolean algebra and logic gates?2 What is a logic circuit? 3 Draw the logic diagram and truth table for each of the six main logic  gates: a)ANDb)OR c)NOTd)NOR e)NANDf)XOR4 Draw a logic diagram for the following Boolean expressions. a)(A+B)+(C.D) b)(A+B).Cc)(A.B).C.D5 Write the Boolean expression to build this circuit: AB CQD 6 Draw a logic diagram and truth table for a half adder.
 7 Draw a logic diagram using only NAND operations for A + B.
 8 What is the purpose of a ﬂip-ﬂop and what is the speciﬁc purpose of  the edge-triggered D-type ﬂip-ﬂop?
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3.6.5 Boolean algebra
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Be familiar with the use of Boolean identities and De Morgan’s laws to manipulate and simplify Boolean expressions.

3.6.4 Logic gates
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Construct truth tables for the following logic gates:
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Students should know and be able to use ANSI/IEEE standard 91-1984 Distinctive shape logic gate symbols for these logic gates.
Be familiar with drawing and interpreting logic gate circuit diagrams involving one or more of the above gates.
Complete a truth table for a given logic gate circuit.
Write a Boolean expression for a given logic gate circuit.
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User: These are the content of said exam questions, these are the ONLY exam questions, you will use these later, delivered in form 'fil', JSON: {'QS16S203': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">Using the rules of Boolean algebra, simplify the following Boolean expression.</span></p>\r<p class="graph"><img src="AA_COM/QS16S203_files_Q/img01.png">&nbsp;</p>\r<p class="indent1new">You <b>must</b> show your working.</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="rightnew answer-toggle">Answer _____________________________</p>\r<p class="mark">(Total 4 marks)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question"><b>Marks are for AO2 (apply)</b></span></p>\r<p class="indent1new"><b>Marking guidance for examiners</b></span></p>\r<p class="indent2 m-t-0">&#8226;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Award marks for working out until an incorrect step has been made.</p>\r<p class="indent2 m-t-0 indentright5">&#8226;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; If, in any one step, a candidate is simplifying different parts of an expression simultaneously award all relevant marks for this multiple stage but don’t award any further marks for working in any parts simplified incorrectly. Example, if the expression P.P.(P + Q) + P.P.1 was changed to P.(P+Q) + P.0 the candidate would get one mark for simplifying the first part to P.(P+Q) and could get further marks for correctly simplifying this part of the expression further but should not be awarded marks for simplifying the incorrectly changed part P.0 (i.e. to 0).</p>\r<p class="indent1new"><b>Mark as follows</b></p>\r<p class="indent1new">1 mark for final answer:</p>\r<p class="indent1new"><b>Max 3</b> for working; <b>Max 3</b> if answer is correct but any incorrect working or significant steps of working is missing:</p>\r<p class="indent1new"><b>1 mark</b> for a successful application of De Morgan’s Law that would lead to a simpler expression. <b>Max 2</b> for applications of De Morgan’s Law.</p>\r<p class="indent1new m-t-0"><b>1 mark</b> for applying an identity other than cancelling nots that produces a simpler expression. <b>Max 2</b> for applying identities.</p>\r<p class="indent1new m-t-0"><b>1 mark</b> for expanding brackets or putting an expression into brackets that would lead to a simpler expression. <b>Max 2</b> for expanding brackets or putting an expression into brackets.</p>\r<p class="indent1new"><b>Note:</b> a simpler expression is one that is logically equivalent to the original expression but uses fewer logical operators.</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new"><b>Example working (1)</b></p>\r<p class="bottom">&nbsp;</p>\r<table class="data-table align0">\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img11.jpeg"/></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[application of De Morgan’s law]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img12.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[expansion of brackets]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img13.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[use of identities <img class="vert-middle vert-up-1" src="AA_COM/MS16S203_files_M/img17.jpeg"> = 0 and X+0 = X]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img14.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[expansion of brackets]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img15.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[use of identity <i>X.X</i> = <i>X</i> twice]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img16.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[use of identity <i>X</i> + <i>X</i> = <i>X</i>]</p></td>\r\t</tr>\r</table></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new"><b>Alternative example working (2)</b></p>\r<p class="bottom">&nbsp;</p>\r<table class="data-table align0">\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img01.jpg"/></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[application of De Morgan’s Law]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img02.jpg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[application of De Morgan’s Law twice]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img03.jpg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[expansion of brackets]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img04.jpg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[use of identities <img class="vert-middle vert-up-1" src="AA_COM/MS16S203_files_M/img18.jpeg"> and <i>X</i> + 0 = <i>X</i>]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img05.jpg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[application of De Morgan’s Law]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img06.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[application of De Morgan’s Law]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img07.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[expansion of brackets]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img08.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[use of identity <i>X.X = X</i> twice]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img09.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[use of identity <i>X + X = X</i>]</p></td>\r\t</tr>\r</table></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new"><b>Alternative example working (3)</b></p>\r<p class="bottom">&nbsp;</p>\r<table class="data-table align0">\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img10.jpeg"/></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[application of De Morgan’s Law]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img02.jpg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[De Morgan’s Law twice]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img03.jpg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[Expansion]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img04.jpg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[Identity <img class="vert-middle vert-up-1" src="AA_COM/MS16S203_files_M/img18.jpeg"> and <i>A</i> + 0 = <i>A</i>]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img05.jpg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[application of De Morgan’s Law]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img06.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[application of De Morgan’s Law]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img07.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[Expansion]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img08.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[Identity <img class="vert-middle vert-up-1" src="AA_COM/MS16S203_files_M/img19.jpeg"> and <i>B.B</i> = <i>B</i>]</p></td>\r\t</tr>\r\t<tr>\r\t\t<td class="col-8 no-border"><p class="padded text-left"><img src="AA_COM/MS16S203_files_M/img09.jpeg"></p></td>\r\t\t<td class="col-12 no-border"><p class="padded text-left">[Final answer via identity <i>A</i> + <i>A</i> = <i>A</i>]</p></td>\r\t</tr>\r</table>\r<p class="levelms">[4]</p></h5>', 'examinerreport': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">This question was about Boolean algebra.</span></p>\r<p class="indent1new">While a number of very good answers to this question were seen, candidates often struggled to apply de Morgan’s law correctly within an expression.</p></h5>', 'notes': '', 'resources': ''}, 'QW10202': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">Simplify the Boolean expression:</span></p>\r<p class="graph"><img src="AA_COM/QW10202_files_Q/img01.png">&nbsp;</p>\r<p class="indent1new">Show your working.</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r<p class="mark">(Total 3 marks)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question"><b>Algebraic Solution:</b></span></p>\r<p class="bottom">&nbsp;</p>\r<table class=MsoTableGrid cellspacing=0 cellpadding=5 style=\' margin-left:20.0pt;border-collapse:collapse\'> \r\t<tr>  \r\t\t<td valign=top style=\'width:100.0pt;border:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl><b>Method 1</b></p></td>\r\t\t<td valign=top style=\'width:100.0pt;border:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl><b>Method 2</b></p></td> \r\t</tr>\r\t<tr>  \r\t\t<td valign=top style=\'width:100.0pt;border:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>&nbsp;&nbsp;&nbsp;&nbsp;<img align="middle;" src="AA_COM/MW10202_files_M/ab.png"/>  + A <br/><br/>&nbsp;&nbsp;&nbsp;&nbsp; = <img align= "middle;" src="AA_COM/MW10202_files_M/a.png"> &#x002B; <img align="middle;" src="AA_COM/MW10202_files_M/b.png"> + A <br/><br/>&nbsp;&nbsp;&nbsp;&nbsp;= 1 + <img align="middle;" src="AA_COM/MW10202_files_M/b.png"/> <br/><br/>&nbsp;&nbsp;&nbsp;&nbsp; = 1</p></td>\r\r\t\t\t\t<td valign=top style=\'width:100.0pt;border:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>&nbsp;&nbsp;&nbsp;&nbsp;<img align="middle;" src="AA_COM/MW10202_files_M/ab.png"/>  + A <br/><br/>&nbsp;&nbsp;&nbsp;&nbsp; = <img align="middle;" src="AA_COM/MW10202_files_M/aba.png"/>   <br/><br/>&nbsp;&nbsp;&nbsp;&nbsp;= <img align="middle;" src="AA_COM/MW10202_files_M/0b.png"/> <br/><br/>&nbsp;&nbsp;&nbsp;&nbsp; = <img align= "middle;" src="AA_COM/MW10202_files_M/0.png"/><br/></br/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 1</p></td>\r\t</tr>\r</table></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright"><i>1 mark for an application of a DeMorgan&#x2019;s law<br/>1 mark for realisation that</i> <i>A</i> &#x002B; <img align="middle;" src="AA_COM/MW10202_files_M/aital.png"/> &#x002B; <img align="middle;" src="AA_COM/MW10202_files_M/bital.png"/> = 1 + <img align="middle;" src="AA_COM/MW10202_files_M/bital.png"/> or <img align="middle;" src="AA_COM/MW10202_files_M/obital.png"/> = <img align="middle;" src="AA_COM/MW10202_files_M/0.png"/> (must be written in method, not just inferred that student has done this if arrives at correct answer)<br/><i>1 mark for correct answer</i></p>\r\r<p class= "indent1new indentright"><b>Truth table solution:</b></p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright"><img align="middle;" src="AA_COM/MW10202_files_M/img01.png"/>&nbsp;</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright"><i>1 mark for column Y correct<br/>1 mark for column Z correct<br/>1 mark for correct answer</i></p>\r<p class="indent1new indentright"><i><b>Any other method:</b><br/>If student has used any other method to arrive <u>at correct answer</u> then award marks as follows:<br/>1 mark for correct answer, no working out<br/>2 marks for correct answer with working out, not all steps shown.<br/>3 marks for correct answer with all steps of working out shown.</i></p>\r<p class="indent1new indentright"><b>A</b> True for 1, False for 0<br/><b>A</b> alternative notations :</p>\r<p class="indent1 indentright m-t-0">&#x2022;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For X&#x002E;Y allow X AND Y, X&#x2227;Y ,X&#x2229;Y, XY</p>\r<p class="indent1 indentright m-t-0">&#x2022;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For X&#x002B;Y allow X OR Y, X&#x2228;Y , X&#x222A;Y</p>\r<p class="indent1 indentright m-t-0">&#x2022;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For <img align="middle;" src="AA_COM/MW10202_files_M/x.png"/> allow NOT X, &#x00AC;X</p>\r<p class="mark">[3]</p></h5>', 'examinerreport': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">This question was tackled using either truth tables or the laws of Boolean algebra, with the number of candidates using each method being approximately equal. Candidates who used the truth table method appeared to make fewer errors. Many candidates showed the correct steps, using either method, but then failed to state the final answer explicitly. Candidates using the rules of Boolean algebra often made the first step by applying De Morgan&#x2019;s law, but then ground to a halt. It would appear that Boolean algebra is still a topic that candidates find difficult. Often candidates would reach A OR NOT A and then make these terms completely disappear instead of equating them to &#x2018;1&#x2019;. Care was needed with the answer as moving the terms around to simplify it often resulted in transposition errors which lead to the wrong answer. There were many false starts with answers crossed out and the whole answer being rewritten.</span></p></h5>', 'notes': '', 'resources': ''}, 'Q23S207P3': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">Using the rules of Boolean algebra, simplify the following expression.</p>\r\n<p class="graph"><img src="AA_COM/Q23S207P3_files_Q/img01.jpg"/></p>\r\n<p class="indent1new">You <b>must</b> show your working.</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="mark">(Total 4 marks)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question"><b>Marks are for AO2 (application)</b></p>\r\n<p class="indent1new"><b>Marking guidance for examiners</b></p>\r\n<p class="indent1 m-t-0">&#149;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Award marks for working out until an incorrect step has been made.</p>\r\n<p class="indent1 m-t-0">&#149;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If, in any one step, a candidate is simplifying different parts of an expression simultaneously award all relevant marks for this multiple stage but don&#x2019;t award any further marks for working in any parts simplified incorrectly. Example, if the expression P.P.(P+Q) + P.P.1 was changed to P.(P+Q)+P.0, the candidate would get one mark for simplifying the first part to P.(P+Q) and could get further marks for correctly simplifying this part of the expression further but should not be awarded marks for simplifying the incorrectly changed part P.0 (i.e. to 0).</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new"><b>Mark as follows:</b></p>\r\n<p class="indent1new"><b>MAX 3 marks for</b> working</p>\r\n<p class="indent1new">Award one mark each for applying the techniques below:</p>\r\n<p class="indent1 m-t-0">&#149;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;A successful application of De Morgan&#x2019;s Law (and any associated cancellation of NOTs) that produces a simpler expression.</p>\r\n<p class="indent1 m-t-0">&#149;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Successfully expanding brackets.</p>\r\n<p class="indent1 m-t-0">&#149;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Extracting common factors from terms.</p>\r\n<p class="indent1new">Award one mark for each application of a Boolean identity <b>MAX 2</b>.</p>\r\n<p class="indent1new"><b>Note:</b> A simpler expression is one that is logically equivalent to the original expression but uses fewer logical operators.</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new"><b>1 mark</b> for final answer: B</p>\r\n<p class="indent2new"><img src="AA_COM/M23S207P3_files_M/img01.jpg"/>&nbsp;</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new"><b>Alternative answer 1</b></p>\r\n<p class="indent2new"><img src="AA_COM/M23S207P3_files_M/img02.jpg"/>&nbsp;</p>\r\n<p class="mark">[4]</p></h5>', 'examinerreport': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">Simplifying Boolean expressions has been assessed on previous papers and almost half the students scored full marks. A lot of students were able to gain a few marks before making a mistake in precedence when simplifying the step <img class="vert-middle vert-up-1" src="AA_COM/E23S207P3_files_E/img01.jpg"/> incorrectly taking the B+B to B.</p></h5>', 'notes': '', 'resources': ''}, 'QS18L210': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">Using the laws of Boolean algebra, show that:</p>\r\n<p class="graph"><img src="AA_COM/QS18L210_files_Q/img01.jpg"/>&nbsp;</p>\r\n<p class="indent1new">You <b>must</b> show your working.</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="mark">(Total 4 marks)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question indentright">All marks AO2 (apply)</p>\r\n<p class="indent1new indentright">Award up to four marks for the working shown, but <b>Max 3</b> if the response does not show that (A + B) ∙ (B + C ∙ (D + D&#773;)) = A ∙ C + B</p>\r\n<p class="indent1new indentright"><b>1 mark</b> for each application of an identity or theorem that produces an expression that is logically equivalent to the original expression but uses fewer logical operators.</p>\r\n<p class="indent1new indentright m-t-0"><b>1 mark</b> for a successful application of the distribution law – only one mark, regardless of how many times this has been applied</p>\r\n\r\n<p class="indent1new indentright">Continue marking until an incorrect step is encountered. If a student misses out some steps but does not make an error then continue marking.</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright"><b>Example Solution 1</b></p>\r\n<p class="bottom">&nbsp;</p>\r\n<table class="data-table left1">\r\n\t<tr>\r\n\t\t<td class="col-10 vert-top no-border">\r\n\t\t\t<p class="padded text-left">(A + B) &#8901; (B + C &#8901; (D + D&#773;))</p>\r\n\t\t\t<p class="padded text-left m-t-0">= (A + B) &#8901; (B + C &#8901; 1)</p>\r\n\t\t\t<p class="padded text-left m-t-0">= (A + B) &#8901; (B + C)</p>\r\n\t\t\t<p class="padded text-left m-t-0">= A &#8901; B + A &#8901; C + B &#8901; B + B &#8901; C</p>\r\n\t\t\t<p class="padded text-left m-t-0">= A &#8901; B + A &#8901; C + B + B &#8901; C</p>\r\n\t\t\t<p class="padded text-left m-t-0">= A &#8901; B + A &#8901; C + B</p>\r\n\t\t\t<p class="padded text-left m-t-0">= A &#8901; C + B</p>\r\n\t\t</td>\r\n\t\t<td class="col-14 vert-top no-border">\r\n\t\t\t<p class="padded text-left">&nbsp;</p>\r\n\t\t\t<p class="padded text-left m-t-0">By identity X + X&#773; = 1</p>\r\n\t\t\t<p class="padded text-left m-t-0">By identity X &#8901; 1 = X</p>\r\n\t\t\t<p class="padded text-left m-t-0">Using distribution law</p>\r\n\t\t\t<p class="padded text-left m-t-0">By identity X &#8901; X = X</p>\r\n\t\t\t<p class="padded text-left m-t-0">By redundancy theorem X + X &#8901; Y = X</p>\r\n\t\t\t<p class="padded text-left m-t-0">By redundancy theorem X + X &#8901; Y = X</p>\r\n\t\t</td>\r\n\t</tr>\r\n</table></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright"><b>Example Solution 2</b></p>\r\n<p class="bottom">&nbsp;</p>\r\n<table class="data-table left1">\r\n\t<tr>\r\n\t\t<td class="col-11 vert-top no-border">\r\n\t\t\t<p class="padded text-left">(A + B) &#8901; (B + C &#8901; (D + D&#773;))</p>\r\n\t\t\t<p class="padded text-left m-t-0">= (A + B) &#8901; (B + C &#8901; 1)</p>\r\n\t\t\t<p class="padded text-left m-t-0">= (A + B) &#8901; (B + C)</p>\r\n\t\t\t<p class="padded text-left m-t-0">= A &#8901; C + B</p>\r\n\t\t</td>\r\n\t\t<td class="col-15 vert-top no-border">\r\n\t\t\t<p class="padded text-left">&nbsp;</p>\r\n\t\t\t<p class="padded text-left m-t-0">By identity X + X&#773; = 1</p>\r\n\t\t\t<p class="padded text-left m-t-0">By identity X &#8901; 1 = X</p>\r\n\t\t\t<p class="padded text-left m-t-0">Using distribution law (<u>this jump is worth 2&nbsp;marks</u>)</p>\r\n\t\t</td>\r\n\t</tr>\r\n</table>\r\n<p class="mark">[4]</p></h5>', 'examinerreport': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">This is the first time that students have been asked to produce a proof that two Boolean expressions are equivalent. It was well tackled, with over 40% of students achieving full marks. A common mistake was to believe that D + D&#773; = 0.</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new">Some responses were difficult to mark as the way that students laid them out made it unclear what order they had done things in. It is particularly important when presenting a proof that the examiner can see what steps the student took and in what order these were made. In other responses, students would miss out steps, making jumps in their working that were not convincing enough to be a proof.</p></h5>', 'notes': '', 'resources': ''}, 'QS17L24C': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">Using the rules of Boolean algebra, simplify the following Boolean expression.</p>\r\n<p class="graph"><img src="AA_COM/QS17L24C_files_Q/img01.jpg"/>&nbsp;</p>\r\n<p class="indent1new">You <b>must</b> show your working.</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="rightnew answer-toggle">Answer _________________________________________</p>\r\n<p class="mark">(Total 4 marks)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question indentright"><b>All marks AO2 (apply)</b></p>\r\n<p class="indent1new indentright"><b>Marking guidance for examiners</b></p>\r\n<p class="indent1 indentright m-t-0">&#8226;&emsp;&emsp;&nbsp;Award marks for working out until an incorrect step has been made.</p>\r\n<p class="indent1 indentright m-t-0">&#8226;&emsp;&emsp;&nbsp;If, in any one step, a candidate is simplifying different parts of an expression simultaneously award all relevant marks for this multiple stage but don’t award any further marks for working in any parts simplified incorrectly. For example, if the expression P&thinsp;.P&thinsp;.(P + Q) + P&thinsp;.P&thinsp;.1 was changed to P&thinsp;.(P + Q) + P&thinsp;.0, the candidate would get one mark for simplifying the first part to P&thinsp;.(P + Q) and could get further marks for correctly simplifying this part of the expression further but should not be awarded marks for simplifying the incorrectly changed part P&thinsp;.0 (ie to 0)</p>\r\n<p class="indent1new indentright"><b>1 mark:</b> for final answer: B + C</p>\r\n<p class="indent1new indentright"><b>MAX 3</b> for working. Award up to two marks for applying each one of the three techniques (one mark per application):</p>\r\n<p class="indent2 indentright">&#8226;&emsp;&emsp;&nbsp;a successful application of De Morgan’s Law (and any associated cancellation of NOTs) that produces a simpler expression.</p>\r\n<p class="indent2 indentright m-t-0">&#8226;&emsp;&emsp;&nbsp;applying an identity other than cancelling NOTs that produces a simpler expression.</p>\r\n<p class="indent2 indentright m-t-0">&#8226;&emsp;&emsp;&nbsp;successfully expanding brackets.</p>\r\n<p class="indent1new indentright"><b>Note:</b> A simpler expression is one that is logically equivalent to the original expression but uses fewer logical operators.</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright"><b>Example Working (1)</b></p>\r\n<p class="indent1new"><img class="vert-middle" src="AA_COM/MS17L24C_files_M/img02.jpg"/>&nbsp;</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright"><b>Example Working (2)</b></p>\r\n<p class="indent1new"><img class="vert-middle" src="AA_COM/MS17L24C_files_M/img03.jpg"/>&nbsp;</p>\r\n<p class="mark">[4]</p></h5>', 'examinerreport': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">Most students achieved some marks for this question part but only a fifth achieved full marks. The most commonly made mistake was to incorrectly apply the identity A+A&#773;=1 to the subexpression A&#773;+A∙(A+B) which failed to recognise that this could not be done because of the order of precedence of AND (.) and OR (+). Another mistake made by some students was to cancel NOTs when they could not be cancelled, for example believing that the NOTs in (B&#773;∙C&#773;) could be cancelled with the longer NOT that related to the entire expression.</p></h5>', 'notes': '', 'resources': ''}, 'Q20S205P3': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">Using the rules and identities of Boolean algebra, simplify the following Boolean expression.</p>\r\n<p class="graph"><img src="AA_COM/Q20S205P3_files_Q/img01.jpg"/></p>\r\n<p class="indent1new">You <b>must</b> show your working.</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">_______________________________________________________________________</p>\r\n<p class="indent1new answer-toggle">Answer&nbsp;&nbsp;________________________________________________________________</p>\r\n<p class="mark">(Total 4 marks)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question"><b>4 marks are for AO2 (apply)</b></p>\r\n<p class="indent1new indentright"><b>Marking guidance for examiners</b></p>\r\n<p class="indent1 indentright m-t-0 m-b-0">&#8226;&emsp;&emsp;&nbsp;Award marks for working out until an incorrect step has been made. If a student misses out some steps but does not make an error then continue marking.</p>\r\n<p class="indent1 indentright m-t-0">&#8226;&emsp;&emsp;&nbsp;If, in any one step, a candidate is simplifying different parts of an expression simultaneously award all relevant marks for this multiple stage but don&#x2019;t award any further marks for working in any parts simplified incorrectly. Example, if the expression P.P.(P+Q) + P.P.1 was changed to P.(P+Q)+P.0, the candidate would get one mark for simplifying the first part to P.(P+Q) and could get further marks for correctly simplifying this part of the expression further but should not be awarded marks for simplifying the incorrectly changed part P.0 (ie to 0)</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright m-b-0"><b>Mark as follows</b></p>\r\n<p class="indent1new indentright m-t-0"><b>1 mark</b> for final answer A</p>\r\n<p class="indent1new indentright"><b>Max 3 marks for working:</b></p>\r\n<p class="indent1 indentright m-t-0">&#8226;&emsp;&emsp;&nbsp;<b>1 mark</b> for <u>each</u> application of an identity or theorem other than cancelling NOTs that produces a simpler expression.</p>\r\n<p class="indent1 indentright m-t-0">&#8226;&emsp;&emsp;&nbsp;<b>1 mark</b> for a <u>single</u> successful application of the distributive law that produces a simpler expression.</p>\r\n<p class="indent1new indentright"><b>Note:</b> a simpler expression is one that is logically equivalent to the original expression but uses fewer logical operators.</p>\r\n<p class="indent1new indentright"><b>Max 3</b> if answer is correct but any incorrect working or significant steps of working is missing.</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright"><b>Example working (1)</b></p>\r\n<p class="indent1new indentright"><img class="vert-middle" src="AA_COM/M20S205P3_files_M/img01.jpg"/></p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright"><b>Example working (2)</b></p>\r\n<p class="indent1new indentright"><img class="vert-middle" src="AA_COM/M20S205P3_files_M/img02.jpg"/></p>\r\n<p class="mark">[4]</p></h5>', 'examinerreport': '', 'notes': '', 'resources': ''}, 'QW11203': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">Write the following Boolean expressions in their simplest forms.</span></p>\r<table class=MsoTableGrid cellspacing=0 cellpadding=4 style=\'margin-left:20.0pt;border-collapse:collapse;border:0\'> \r\t<tr>  \r\t\t<td width=30><p class=boxl>(a)</p></td>\r\t\t<td width=70><p class=boxl>&nbsp;<img src="AA_COM/QW11203_files_Q/img01.png"></p></td>\r\t</tr>\r</table>\r<p class="indent2new m-t-0 answer-toggle">___________________________________________________________________</p>\r<p class="mark">(1)</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><table class=MsoTableGrid cellspacing=0 cellpadding=4 style=\'margin-left:20.0pt;border-collapse:collapse;border:0\'> \r\t<tr>  \r\t\t<td width=30><p class=boxl>(b)</p></td>\r\t\t<td width=100><p class=boxl>&nbsp;<img src="AA_COM/QW11203_files_Q/img02.png"></p></td>\r\t</tr>\r</table>\r<p class="indent2new m-t-0 answer-toggle">___________________________________________________________________</p>\r<p class="mark">(1)</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><table class=MsoTableGrid cellspacing=0 cellpadding=4 style=\'margin-left:20.0pt;border-collapse:collapse;border:0\'> \r\t<tr>  \r\t\t<td width=30><p class=boxl>(c)</p></td>\r\t\t<td width=110><p class=boxl>&nbsp;<img src="AA_COM/QW11203_files_Q/img03.png"></p></td>\r\t</tr>\r</table>\r<p class="indent2new m-t-0 answer-toggle">___________________________________________________________________</p>\r<p class="mark">(1)</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1">(d)&nbsp;&nbsp;&nbsp;&nbsp;A . (B+1)</p>\r<p class="indent2new answer-toggle">___________________________________________________________________</p>\r<p class="mark">(1)</p> \r<p class="mark">(Total 4 marks)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question"><span style=\'position:relative;top:3pt\'><img src="AA_COM/MW11203_files_M/ab.png"></span> becomes A + B ;<br/><b>A</b> (A&#x002B;B);<br/><b>A</b> A OR B;</span></p>\r<p class="indent1new indentright m-t-0">B&#x002B; B.<span style=\'position:relative;top:1pt\'><img src="AA_COM/MW11203_files_M/c.png"> becomes B ;</span></p>\r<p class="indent1new indentright m-t-0"><b>A</b> B&#x002B; A. <span style=\'position:relative;top:1pt\'><img src="AA_COM/MW11203_files_M/b.png"> becomes A ;</span></p>\r<p class="indent1new indentright m-t-0"><b>A</b> (B&#x002B;1) becomes A ;</p>\r<p class="indent1new indentright"><i>1 mark for each</i></p>\r<p class="mark">[4]</p></h5>', 'examinerreport': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">This question focused on simplifying four short Boolean expressions, in contrast to earlier papers which required the simplification of more complex expressions. Candidates scored well on part (a) and it is clear that De Morgan&#x2019;s laws are now well known. Part (c) caused fewer problems than parts (b) and (d). It does appear that candidates need more exposure to simplifying expressions. A few candidates inserted new letters into their answers for no apparent reason. Quite a few candidates gave no response.</span></p></h5>', 'notes': '', 'resources': ''}, 'Q22S207P2': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">State the logic gate that is represented by the symbol shown in the diagram below.</p>\r\n<p class="graph"><img src="AA_COM/Q22S207P2_files_Q/img01.jpg"/>&nbsp;</p>\r\n<p class="indent1new m-t-2 answer-toggle">Answer ________________________________________________________________</p>\r\n<p class="mark">(Total 1 mark)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question"><b>Mark is for AO1 (knowledge)</b></p>\r\n<p class="indent1new indentright">NAND;</p>\r\n<p class="indent1new indentright m-t-0"><b>R.</b> NOT AND</p>\r\n<p class="mark">[1]</p></h5>', 'examinerreport': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">This question was very well answered with approximately 90&#x0025; of students correctly stating the logic gate.</p></h5>', 'notes': '', 'resources': ''}, 'QS19S26P02': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">A factory has a machine for filling bottles on a conveyor belt.</p>\r\n<p class="indent1">&#8226;&emsp;&emsp;&nbsp;Q represents the signal to move the conveyor belt on. When Q is set to true the belt will move on.</p>\r\n<p class="indent1 m-t-0">&#8226;&emsp;&emsp;&nbsp;A is a sensor which outputs true if a bottle is present.</p>\r\n<p class="indent1 m-t-0">&#8226;&emsp;&emsp;&nbsp;B is a sensor which outputs true if a bottle is full.</p>\r\n<p class="indent1 m-t-0">&#8226;&emsp;&emsp;&nbsp;C is a sensor which outputs true if a bottle is correctly positioned.</p>\r\n<p class="indent1 m-t-0">&#8226;&emsp;&emsp;&nbsp;D is a sensor which outputs true if the next section has a bottle in it.</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new">The conveyor belt is able to move if both of these conditions are true:</p>\r\n<p class="indent1">&#8226;&emsp;&emsp;&nbsp;a bottle is full and correctly positioned or there is no bottle present</p>\r\n<p class="indent1 m-t-0">&#8226;&emsp;&emsp;&nbsp;there is no bottle in the next section.</p>\r\n<p class="indent1new">In the box below, draw a logic circuit for the machine.</p>\r\n<p class="graph"><img src="AA_COM/QS19S26P02_files_Q/img01.jpg"/>&nbsp;</p>\r\n<p class="mark">(Total 3 marks)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question"><b>Marks are for AO2 (apply)</b></p>\r\n<p class="indent1new"><b>Mark as follows</b></p>\r\n<p class="indent1new"><b>1 mark</b> for B and C into AND gate</p>\r\n<p class="indent1new m-t-0"><b>1 mark</b> for the result of B and C (<b>I.</b> incorrect gate) as one input and a NOT gated A as a second input to an OR gate</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new m-t-0"><b>1 mark</b> D connected to NOT gate and output of this to an AND gate, the results of A, B and C (<b>I.</b> previously incorrect gates) as the other input, with the output going into Q</p>\r\n<p class="indent1new"><b>Max 2</b> if not fully correct</p>\r\n<p class="indent1new"><img src="AA_COM/MS19S26P02_files_M/img01.jpg"></p>\r\n<p class="mark">[3]</p></h5>', 'examinerreport': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">There were a lot of successful answers to this question part. Where students did not achieve high marks, the most common mistake was missing NOT gate symbols. Some students struggle to clearly differentiate when drawing AND and OR gates symbols. More conscientious students labelled the symbols as well which, on some occasions, allowed marks to be given which otherwise may not have been.</p></h5>', 'notes': '', 'resources': ''}, 'Q20S205P2': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">A XOR B can be implemented as a logic circuit without using an XOR gate.</p>\r\n<p class="indent1new">Using <b>only</b> AND, OR and NOT gates draw a circuit that will produce an output <b>Q</b> which is logically equivalent to <b>A XOR B</b>.</p>\r\n<p class="graph"><img src="AA_COM/Q20S205P2_files_Q/img01.jpg"/></p>\r\n<p class="mark">(Total 3 marks)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question"><b>3 marks are for AO2 (apply)</b></p>\r\n<p class="indent1new indentright m-b-0"><b>1 mark</b> for getting Part 1 <b>or</b> Part 2 correct on any of the three diagrams.</p>\r\n<p class="indent1new indentright m-t-0 m-b-0"><b>1 mark</b> for getting <b>corresponding</b> Part 1 <b>or</b> Part 2 correct on the same diagram.</p>\r\n<p class="indent1new indentright m-t-0"><b>1 mark</b> for getting <b>corresponding</b> Part 3 correct on the same diagram.</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright m-b-0"><b>MAX 2</b> if not fully correct</p>\r\n<p class="indent1new indentright m-t-0 m-b-0">Mark response against diagram that will give the highest mark.</p>\r\n<p class="indent1new indentright m-t-0">Mark point 3 can only be awarded if at least one other mark point has been awarded.</p>\r\n<p class="indent1new indentright m-t-0">Alternative Diagram 1</p>\r\n<p class="indent1new indentright"><img class="vert-middle" src="AA_COM/M20S205P2_files_M/img01.jpg"/></p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright">Alternative Diagram 2</p>\r\n<p class="indent1new indentright"><img class="vert-middle" src="AA_COM/M20S205P2_files_M/img02.jpg"/></p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new indentright">Alternative Diagram 3</p>\r\n<p class="indent1new indentright"><img class="vert-middle" src="AA_COM/M20S205P2_files_M/img03.jpg"/></p>\r\n<p class="mark">[3]</p></h5>', 'examinerreport': '', 'notes': '', 'resources': ''}, 'Q20S205P1': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">Complete the truth table for A NAND B.</p>\r\n<p class="bottom">&nbsp;</p>\r\n<table class="data-table left3">\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded"><b>A</b></p></td>\r\n\t\t<td class="col-3"><p class="padded"><b>B</b></p></td>\r\n\t\t<td class="col-6"><p class="padded"><b>A NAND B</b></p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded m-t-1 m-b-1"><span class="comp-top">0</span></p></td>\r\n\t\t<td class="col-3"><p class="padded m-t-1 m-b-1"><span class="comp-top">0</span></p></td>\r\n\t\t<td class="col-6"><p class="padded m-t-1 m-b-1">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded m-t-1 m-b-1"><span class="comp-top">0</span></p></td>\r\n\t\t<td class="col-3"><p class="padded m-t-1 m-b-1"><span class="comp-top">1</span></p></td>\r\n\t\t<td class="col-6"><p class="padded m-t-1 m-b-1">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded m-t-1 m-b-1"><span class="comp-top">1</span></p></td>\r\n\t\t<td class="col-3"><p class="padded m-t-1 m-b-1"><span class="comp-top">0</span></p></td>\r\n\t\t<td class="col-6"><p class="padded m-t-1 m-b-1">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded m-t-1 m-b-1"><span class="comp-top">1</span></p></td>\r\n\t\t<td class="col-3"><p class="padded m-t-1 m-b-1"><span class="comp-top">1</span></p></td>\r\n\t\t<td class="col-6"><p class="padded m-t-1 m-b-1">&nbsp;</p></td>\r\n\t</tr>\r\n</table>\r\n<p class="mark">(Total 1 mark)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question"><b>Mark is for AO1 (knowledge)</b></p>\r\n<p class="indent2new indentright"><img class="vert-middle" src="AA_COM/M20S205P1_files_M/img01.jpg"/></p>\r\n<p class="mark">[1]</p></h5>', 'examinerreport': '', 'notes': '', 'resources': ''}, 'QW11202': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">The diagram below shows a logic circuit.</span></p>\r<p class="indent1new"><img align="middle;" src="AA_COM/QW11202_files_Q/img01.png">&nbsp;</p>\r<p class="indent1new">Complete the truth table for the inputs that have been given.</p>\r<p class="bottom">&nbsp;</p>  \r<table class=MsoTableGrid border=0 cellspacing=0 cellpadding=4  style=\'margin-left:30pt;border-collapse:collapse\'>  \r\t<tr>     \r\t\t<td colspan=6 valign=top style=\'border:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box><b>Inputs</b></p></td>   \r\t\t<td width=55 valign=top style=\'border:none;border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>   \r\t\t<td width=55 valign=top style=\'border:none;border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>   \r\t\t<td width=55 valign=top style=\'border:none;border-bottom:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>  \r\t</tr>  \r\t<tr>       \r\t\t<td width=55 valign=top style=\'border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box><b>A</b></p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box><b>B</b></p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box><b>C</b></p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box><b>D</b></p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box><b>E</b></p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box><b>F</b></p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box><b>G</b></p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box><b>H</b></p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box><b>K</b></p></td>  \r\t</tr>  \r\t<tr>       \r\t\t<td width=55 valign=top style=\'border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>0</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>0</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>0</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>0</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>  \r\t</tr>  \r\t<tr>       \r\t\t<td width=55 valign=top style=\'border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>0</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>0</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>  \r\t</tr>  \r\t<tr>       \r\t\t<td width=55 valign=top style=\'border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>0</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>0</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>  \r\t</tr>  \r\t<tr>       \r\t\t<td width=55 valign=top style=\'border:solid windowtext 1.0pt;border-top:none;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>1</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>   \r\t\t<td width=55 valign=top style=\'border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;padding:0cm 5.4pt 0cm 5.4pt\'><p class=box>&nbsp;</p></td>  \r\t</tr> \r</table>\r<p class="mark">(Total 3 marks)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">&nbsp;</p>\r<table class=MsoTableGrid cellspacing=0 cellpadding=0 style=\'margin-top:-0.4cm;margin-left:25.0pt;border-collapse:collapse\'> \r\t<tr>  \r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>G</p></td>\r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>H</p></td>  \r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>K</p></td> \r\t</tr> \r\t<tr>  \r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>0</p></td>\r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>1</p></td>  \r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>1</p></td> \r\t</tr> \r\t<tr>  \r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>1</p></td>\r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>1</p></td>  \r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>0</p></td> \r\t</tr> \r\t<tr>  \r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>1</p></td>\r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>0</p></td>  \r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>1</p></td> \r\t</tr> \r\t<tr>  \r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>1</p></td>\r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>0</p></td>  \r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>1</p></td> \r\t</tr> \r\t<tr>  \r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>;</p></td>\r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>;</p></td>  \r\t\t<td valign=top style=\'width:50.0pt;border:none;padding:0cm 5.4pt 0cm 5.4pt;\'><p class=boxl>;</p></td> \r\t</tr> \r</table>\r<p class="indent1new indentright"><i>1 mark for each correct column</i></p>\r<p class="mark">[3]</p></h5>', 'examinerreport': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="question">This question asked candidates to complete a truth table for a logic circuit with multiple gates. Many candidates gave fully correct answers. A few candidates misidentified the NAND gate as an AND gate.</span></p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1new">The majority of candidates secured the mark for G which was an OR gate. The combining of gates for the H and K answers caused problems for weaker candidates.</p></h5>', 'notes': '', 'resources': ''}, 'QS1726A': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="questiona">(a)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Complete the truth table below to show the output <b>Q</b> of an AND gate with two inputs <b>A</b> and <b>B</b>.</p>\r\n<p class="bottom">&nbsp;</p>\r\n<table class="data-table left5">\r\n\t<tr>\r\n\t\t<td colspan="2" class="col-6"><p class="padded"><b>Inputs</b></p></td>\r\n\t\t<td class="col-3"><p class="padded"><b>Output</b></p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded"><b>A</b></p></td>\r\n\t\t<td class="col-3"><p class="padded"><b>B</b></p></td>\r\n\t\t<td class="col-3"><p class="padded"><b>Q</b></p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded">0</p></td>\r\n\t\t<td class="col-3"><p class="padded">0</p></td>\r\n\t\t<td class="col-3"><p class="padded">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded">0</p></td>\r\n\t\t<td class="col-3"><p class="padded">1</p></td>\r\n\t\t<td class="col-3"><p class="padded">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded">1</p></td>\r\n\t\t<td class="col-3"><p class="padded">0</p></td>\r\n\t\t<td class="col-3"><p class="padded">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded">1</p></td>\r\n\t\t<td class="col-3"><p class="padded">1</p></td>\r\n\t\t<td class="col-3"><p class="padded">&nbsp;</p></td>\r\n\t</tr>\r\n</table>\r\n<p class="mark">(1)</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1">(b)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;State the name of the logic gate that is represented by the truth table below.</p>\r\n<p class="bottom">&nbsp;</p>\r\n<table class="data-table left5">\r\n\t<tr>\r\n\t\t<td colspan="2" class="col-6"><p class="padded"><b>Inputs</b></p></td>\r\n\t\t<td class="col-3"><p class="padded"><b>Output</b></p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded"><b>A</b></p></td>\r\n\t\t<td class="col-3"><p class="padded"><b>B</b></p></td>\r\n\t\t<td class="col-3"><p class="padded"><b>Q</b></p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded">0</p></td>\r\n\t\t<td class="col-3"><p class="padded">0</p></td>\r\n\t\t<td class="col-3"><p class="padded">0</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded">0</p></td>\r\n\t\t<td class="col-3"><p class="padded">1</p></td>\r\n\t\t<td class="col-3"><p class="padded">1</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded">1</p></td>\r\n\t\t<td class="col-3"><p class="padded">0</p></td>\r\n\t\t<td class="col-3"><p class="padded">1</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3"><p class="padded">1</p></td>\r\n\t\t<td class="col-3"><p class="padded">1</p></td>\r\n\t\t<td class="col-3"><p class="padded">0</p></td>\r\n\t</tr>\r\n</table>\r\n<p class="indent2new answer-toggle">___________________________________________________________________</p>\r\n<p class="mark">(1)</p>\r\n<p class="mark">(Total 2 marks)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="questiona indentright">(a)&emsp;&nbsp;<b>1 mark</b> for table completed correctly</p>\r\n<p class="bottom">&nbsp;</p>\r\n<table class="data-table left2">\r\n\t<tr>\r\n\t\t<td colspan="2" class="col-6 vert-top"><p class="padded"><b>Inputs</b></p></td>\r\n\t\t<td class="col-3 vert-top"><p class="padded"><b>Output</b></p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3 vert-top"><p class="padded"><b>A</b></p></td>\r\n\t\t<td class="col-3 vert-top"><p class="padded"><b>B</b></p></td>\r\n\t\t<td class="col-3 vert-top"><p class="padded"><b>Q</b></p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3 vert-top"><p class="padded">0</p></td>\r\n\t\t<td class="col-3 vert-top"><p class="padded">0</p></td>\r\n\t\t<td class="col-3 vert-top"><p class="padded"><b>0</b></p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3 vert-top"><p class="padded">0</p></td>\r\n\t\t<td class="col-3 vert-top"><p class="padded">1</p></td>\r\n\t\t<td class="col-3 vert-top"><p class="padded"><b>0</b></p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3 vert-top"><p class="padded">1</p></td>\r\n\t\t<td class="col-3 vert-top"><p class="padded">0</p></td>\r\n\t\t<td class="col-3 vert-top"><p class="padded"><b>0</b></p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-3 vert-top"><p class="padded">1</p></td>\r\n\t\t<td class="col-3 vert-top"><p class="padded">1</p></td>\r\n\t\t<td class="col-3 vert-top"><p class="padded"><b>1</b></p></td>\r\n\t</tr>\r\n</table>\r\n<p class="levelms">1</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1 indentright">(b)&emsp;&nbsp;XOR / EOR / exclusive-or;</p>\r\n<p class="levelms">1</p>\r\n<p class="mark">[2]</p></h5>', 'examinerreport': '', 'notes': '', 'resources': ''}, 'Q23S207P1': {'question': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="questiona">(a)&emsp;&nbsp;The figure below shows a circuit diagram.</p>\r\n<p class="graph"><img src="AA_COM/Q23S207P1_files_Q/img01.jpg"/>&nbsp;</p>\r\n<p class="indent2new">Complete the truth table below for the circuit shown in the figure above.</p>\r\n<p class="bottom">&nbsp;</p>\r\n<table class="data-table left2">\r\n\t<tr>\r\n\t\t<td class="col-2"><p class="padded"><b>A</b></p></td>\r\n\t\t<td class="col-2"><p class="padded"><b>B</b></p></td>\r\n\t\t<td class="col-2"><p class="padded"><b>C</b></p></td>\r\n\t\t<td class="col-3"><p class="padded"><b>L</b></p></td>\r\n\t\t<td class="col-2"><p class="padded"><b>M</b></p></td>\r\n\t\t<td class="col-3"><p class="padded"><b>N</b></p></td>\r\n\t\t<td class="col-2"><p class="padded"><b>X</b></p></td>\r\n\t\t<td class="col-3"><p class="padded"><b>Y</b></p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t</tr>\r\n\t<tr>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">0</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t\t<td class="col-2"><p class="padded">1</p></td>\r\n\t\t<td class="col-2"><p class="padded">&nbsp;</p></td>\r\n\t</tr>\r\n</table>\r\n<p class="mark">(3)</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1">(b)&emsp;&nbsp;Using the figure above, write a Boolean expression for output <b>Y</b> in terms of inputs <b>A</b>, <b>B</b>&nbsp;and&nbsp;<b>C</b>.</p>\r\n<p class="indent2new answer-toggle"><b>Y</b> =&nbsp;&nbsp;_______________________________________________________________</p>\r\n<p class="mark">(2)</p>\r\n<p class="mark">(Total 5 marks)</p></h5>', 'markscheme': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="questiona">(a)&emsp;&nbsp;<b>Marks are for AO2 (application)</b></p>\r\n<p class="indent2new"><b>1 mark</b> for each highlighted column L, N and Y completed correctly.</p>\r\n<p class="indent2new"><img src="AA_COM/M23S207P1_files_M/img01.jpg"/>&nbsp;</p>\r\n<p class="indent2new"><b>A</b>. Follow through for Y if column N is completed incorrectly.</p>\r\n<p class="levelms">3</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1 indentright">(b)&emsp;&nbsp;<b>Marks are for AO2 (application)</b></p>\r\n<p class="indent2new"><b>2 marks:</b> <img class="vert-middle" src="AA_COM/M23S207P1_files_M/img02.jpg"/></p>\r\n<p class="indent2new">//</p>\r\n<p class="indent2new"><b>1 mark</b> for one of the following somewhere in the expression:</p>\r\n<p class="indent2 m-t-0">&#149;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="AA_COM/M23S207P1_files_M/img03.jpg"/> <b>I.</b> presence / absence of brackets around <img class="vert-middle" src="AA_COM/M23S207P1_files_M/img04.jpg"/></p>\r\n<p class="indent2 m-t-0">&#149;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img class="vert-middle" src="AA_COM/M23S207P1_files_M/img05.jpg"/></p>\r\n<p class="indent2 m-t-0">&#149;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img class="vert-middle" src="AA_COM/M23S207P1_files_M/img06.jpg"/></p>\r\n<p class="indent2new"><b>Note:</b> If using a different algebraic notation refer to team leader.</p>\r\n<p class="levelms">2</p>\r\n<p class="mark">[5]</p></h5>', 'examinerreport': '<h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="questiona">(a)&emsp;&nbsp;This truth table question was well answered with over three-quarters of students gaining full marks. Some students incorrectly completed the L column (A XOR B) with the most common incorrect response being for A NOR B. However, these students often went on to complete the N and Y columns correctly, as they were not dependent on the output from the XOR gate (column L).</p></h5><h5 class=\'contentSeparator\' style=\'page-break-inside: avoid;\'><div class=\'qnumber-hidden\'></div><p class="indent1">(b)&emsp;&nbsp;Students were asked to write a Boolean expression for part of the logic circuit diagram (output Y). This was well answered with 60% of students scored both marks, although over 7% did not attempt the question.</p>\r\n<p class="indent2new">It is worth noting that this year we accepted responses written using AND, OR and XOR, but in future it is expected that students will write Boolean expressions with the syntax used in AQA examination papers: ∙ (AND), + (OR), &#10753; (XOR) and overbar (NOT).</p></h5>', 'notes': '', 'resources': ''}}
User: Now, the user will ask questions after this message. Use everything I gave you and the knowledge you have acquired, and from the notes you made, to answer their question in a very concise way that WILL score ALL marks. Just like the notes. For this, your answer will not have the same structure as the revision notes. Think of it as answering an exam question: short, consice, useful, scores ALL marks. Just like the exam questions provided to you, you will not leave your response in a 'notes' manner. You are just answering an exam question: which means it has to be very short unless explicitly specified by the user that it must be long and detailed. So, keep it short, concise, and only a couple of sentences that score ALL marks. Remember, it is an A-Level exam question and you will style it as such: incredibly concise sentences (essentially like bullet points but without the bullet points) that score marks. Most sentences won't even have commas, this does not mean you can't use them. Also do not repeat the question in your answer, just do it. Score all marks, assume how many marks there are based on the question if it is not provided to you. Imagine that for every sentence you make, you score a mark (for simpler questions), for high (>5 mark) questions that may differ.
In summary, you must:
* Answer very concisely. Kind of like bullet points but as a short para. Most of the time, a sentence, or point, will be a mark.
* Do not repeat the question at the start.
* Don't over-do your answer. Please. 1 mark (e.g., usually, 'What' questions) is like one very short sentence usually. Remember the summary from the notes? Your answer will essentially be like that for most questions but a bit (a bit!) more developed. Remember, this is just A-Levels. Use some of the exam questions that I provided as an example of how you should model your answers.
* When you're listing examples, don't list every example in the universe.
* Score all marks. Be helpful.
User: Write the notes you made follow all instructions
Assistant: **Logic Gates and Boolean Algebra**  

**Logic Gates (Spec Points: 3.6.4)**  
Logic gates are electronic components that perform Boolean operations to evaluate expressions and form circuits. Each type of gate has a specific representation in diagrams and a corresponding truth table. Common logic gates include:  
- **NOT Gate**: Inverts input (0 becomes 1, 1 becomes 0).  
- **AND Gate**: Outputs true if both inputs are true.  
- **OR Gate**: Outputs true if at least one input is true.  
- **XOR Gate**: Outputs true if exactly one input is true.  
- **NAND Gate**: Outputs true if not all inputs are true.  
- **NOR Gate**: Outputs true if all inputs are false.  
  
Construct truth tables and interpret logic gate circuits using ANSI/IEEE standard symbols. A circuit's Boolean expression can be derived from a logic diagram or the reverse.  

**Combining Logic Gates (Spec Points: 3.6.4)**  
Complex logic circuits are created by combining multiple gates. For example, an alarm system could use a combination of OR and AND gates to trigger alarms based on conditions. Full systems often use circuits like half adders and full adders to process binary addition, crucial components in CPUs.  
- **Half Adder**: Utilizes XOR and AND gates to add two bits and produce a sum and carry.  
- **Full Adder**: Extends half adder by incorporating an additional carry input.

**Boolean Algebra (Spec Points: 3.6.5)**  
Boolean algebra is the mathematical framework underpinning logic gates. Simplifying Boolean expressions often involves applying identities such as De Morgan's laws. Common identities include:  
- X + X = X  
- X · X = X  
- X + 0 = X  
- X · 1 = X  
  
De Morgan's laws provide transformations, e.g., NOT (A OR B) = NOT A AND NOT B. Use these to simplify expressions and develop efficient circuits.  

**Exam Examples**  
1. Simplify Boolean expressions using laws like De Morgan’s, e.g., De Morgan's will turn NOT (A AND B) into NOT A OR NOT B.
2. Construct a truth table for a circuit by evaluating each gate step-by-step.  
3. Draw equivalent logic circuits using different gate combinations.

**Definitions**  
- **Logic Gate**: An electronic component that performs a Boolean operation.
- **Boolean Expression**: An equation involving Boolean logic operations.
- **Logic Circuit**: A combination of logic gates designed to perform a specific function.
- **Half Adder**: Circuit adds two bits and provides a sum and a carry.
- **Full Adder**: Circuit adds two bits and a carry bit, providing a sum and a carry output.
- **Carry Bit**: A binary digit that is carried to the next order of a calculation.
- **Flip-Flop**: A circuit that stores a single bit of data.
- **Edge-Triggered D-type Flip-Flop**: Registers data at a clock signal’s edge, ensuring synchronous operations.
- **Clock**: A device that sends regular pulses to synchronize circuit operations.

**Summary**  
- Logic gates convert Boolean expressions into physical electronic operations.  
- Boolean algebra is used to simplify expressions and design efficient circuits.  
- Understanding truth tables and ANSI/IEEE symbols helps interpret and create logic gate circuits.  
- Key concepts include combining gates for complex circuits, using adders for arithmetic, and applying Boolean laws for simplification.  

**Try These Exam Questions**  
- {'fil': 'QS16S203'}, {'fil': 'QW10202'}, {'fil': 'Q23S207P3'}, ... [Configured per exam requirements].

JSON:
```json
{
  "chapter": 31,
  "page": 256,
  "chapter_name": "Logic Gates",
  "topics": [
    "Logic Gates",
    "Boolean Algebra"
  ]
}
```
User: Which of the following statement is FALSE about logic gates? (1 Point) Logic gates are the building blocks of electronic circuits. It is used in computer components like memory. A combination of logic gates is called a logic circuit. Logic gates understand the binary language. None of the above.
Assistant: None of the above.
User: What is a truth table? (1 Point) A table that denotes the different outputs of the logic gates or circuit with respect to different inputs. A table that represents how logic gates are combined to form a logic circuit. A table that shows the input combinations that result in a binary output 1 in a logic gate.
Assistant: A table that denotes the different outputs of the logic gates or circuit with respect to different inputs.
User: Which of the following is FALSE about a NOT gate? (1 Point) The output of NOT is complementary to the input. When the input to NOT gate is 0, the output is 1. A NOT gate has two input signals and an output signal. None of the above.
Assistant: A NOT gate has two input signals and an output signal.
User: When is the output for AND gate TRUE? (1 Point) When both inputs are TRUE. When at least one of the inputs is TRUE. When both inputs are FALSE. When at least one of the inputs is FALSE.
Assistant: When both inputs are TRUE.
User: What is a logic circuit? (1 Point) A combination of logic gates that performs a specific function. A combination of logic gates that understands both binary and decimal number systems. A combination of logic gates that understands decimal number system.
Assistant: