A Binary Numbers Tutorial with 1 and 0 | David J Morgan on Flickr Binary numbers, based on 1s and 0s, reflect the practical essence of computer hardware: electricity is either on or off. Learn how to write in binary numbers, and the (not so secret) code to transform English language letters into binary numbers and back again. When is the letter A not the letter A? Well, computers don't use the letter A. They use the eight character binary number 01000001 to represent A. This binary numbers tutorial describes what binary numbers are and how to calculate them. Computers transport, calculate, and translate binary numbers because computer hardware circuits only have two electrical states, on or off. These two states can be represented as zero (off) or one (on). All letters of the alphabet, numbers, and symbols are converted to eight character binary numbers as you work with them in software on your computer. How you create and translate binary numbers is a good way to learn how computers process data at the lowest level, in their hardware circuits. Also, I provide a free Excel spreadsheet linked at the bottom of this article to help you visualize and calculate binary numbers.

The [Not So] Secret Formula To represent the letter A as 01000001, the computer (and you, to follow along) Â need several basic tools. One tool is an ASCII conversion chart. Without diving into too much technical detail, the ASCII chart maps a unique number between 1 and 255 to all letters of the alphabet capitalized (A-Z) and lower case (a-z), as well as numbers (0-9), spaces, and other special characters. The unique ASCII number that maps to each character, for example, the capital letter A, is used to calculate a unique eight-character binary number, a combination of ones and zeroes like 01000001. It's basically a two-step secret code. The first step is to grab the unique ASCII number for a letter. The second step is to create a unique eight character binary number, a combination of ones and zeroes to represent the ASCII number. And, of course, going from the eight character combination of ones and zeros to the letter or character reverses this process: first turn the binary number into a number between 1 and 255 then use the number to look up the letter in the ASCII chart.

How to Create Binary Numbers Binary numbers are eight characters in length where every character is either a 1 or 0. The placement of each 1 indicates the value of that position, which is used to calculate the total value of the binary number. Each position of each of the eight characters represents a fixed number value, as shown below. Binary Numbers with Values and Positions in a Blank Worksheet If you read these Default Value numbers from bottom to top, can you tell how each number immediately above is calculated? They're doubled. So binary numbers start on the bottom with the first position equal to 1. The second position from the bottom has a value 2, the third position 4, and so on. If you add up all these numbers (1+2+4+8+16+32+64+128), can you guess what number you'll get? 255, the highest number used in the ASCII table. There is a perfect mapping between all possible numbers 1 to 255 in the ASCII table and the calculated values for all possible eight character binary numbers. To calculate the number value of a binary number, add up the value for each position of all the 1s in the eight character number.

The number 01000001, for example, is converted to 64 + 1 or 65. The ones in this binary number are in the first and seventh positions, counting from the bottom to top, or reading right to left. The first position has an assigned value of 1 while the seventh position has an assigned value of 64. Let's Convert a Letter to a Binary Number Now that you know the [not so] secret formula to convert letters to unique ASCII numbers to binary numbers, and how to create binary numbers, let's do the whole process step by step. Let's start with the letter C. First, we need to use an ASCII chart like this one below to look up the unique number assigned to the uppercase letter C. The unique decimal number to use is 67. Decimal DEL To convert the number for C, 67, into a binary number: Remember how binary numbers are read bottom to top, first position and Default Value to top position and Default Value, with each of the eight character positions assigned a unique number value? With the chart below, what combination of values would equal 67?

Binary Numbers with Values and Positions You're correct if you said the Default Values 1 plus 2 plus 64 would equal 67, the ASCII number for the capital letter C. So let's change the first, second, and seventh position zeroes to ones, counted from right to left. The binary number is for the capital letter C is: The letter C as a Binary Number Can you decode this binary number? Add up the 1s to get 64+16+4 or 84. Look up the decimal number 84 in the ASCII chart to find the letter represented below: The letter T as a Binary Number If you converted this binary number to the capital letter T, you're correct.

Here is the letter A as a binary number to represent the ASCII decimal number for A, which is 65: The letter A as a Binary Number If we combine the binary numbers we've looked at so far, we can spell CAT: 01000011 01000001 01010100 Bonus: Pseudo-Code to Design a Binary Number Converter With an understanding of how letters and numbers are converted to binary numbers, and back, let's look at how we might create a software application to make these conversions on the fly. The application has no real value. But it provides a chance to discuss how a process can be converted to software. Instead of actual code, however, we'll write up a series of statements or pseudo-code. Let's take the word cat to start. What process do we need to convert these letters automatically into binary numbers? Here's one possible set of steps we could code: Break the word into individual letters. For each letter, look up the ASCII number value mapped to the letter. For each ASCII number value, convert to a binary number. For each binary number, save the binary number value.

If it is the first binary number, create the initial binary number value; if a binary number value exists, add the new binary number to the end of the value. Imagine if we skipped the last step: what would be the result of these steps? We'd only have the last binary number, for the lower case letter t in cat. It's important we capture each binary number as they are created. Other observations about this pseudo-code process? We need to distinguish between capital letters and lower case letters, don't we? Otherwise, our binary number conversion might translate from binary number to ASCII letters as CAT or cAT or Cat. Our lookup to match letters to the ASCII table might grab the wrong number. Bonus Bonus: A Final Puzzle Can you decode the phrase in this set of binary numbers? Remember, these are eight character blocks of 1s and 0s.

01000011 01101111 01100100 01100101 01101001 01110011 01010000 01101111 01100101 01110100 01110010 01111001 Here’s a fairly easy way to convert any letter into a binary number. Grab a calculator, find the ASCII decimal value for the letter, from the chart above, then look at the binary number chart for the nearest value to the decimal value. Subtract the nearest number Default Value in the binary chart to get a remainder value. Look for the nearest binary Default Value for the remainder. Repeat until you run out of binary values. If you’re clever, you’ll also note the sum of the values below any of the eight Default Values equals one less than the value: so below the binary value 4 are the values 2 and 1 which equal 3.

Below the binary value of 8 are 4, 2, and 1 which equal 7. This also can help convert letters to binary numbers. If your remainder is 7, for example, then you know to put a 1 at the 4, 2, and 1 positions to create that part of your binary number. To convert binary numbers to letters, just grab a piece of paper and a pen or pencil and add up the binary values of all the 1s. Then look up your total number as an ASCII decimal in the chart above. Here’s a hint to help determine if you have solved the binary numbers above correctly: I majored in American poetry in college and love the old tagline used for WordPress publishing software. If you want more binary numbers, check out our article about Bakuro binary number puzzles which work like Sudoku. Learn More The Binary System PDF FILE - CLICK HERE FOR PRINTABLE VERSION OF WORK SEEN BELOW Binary numbers are closely related to digital electronics. With digital electronics a ï¿½1ï¿½ means that current / electricity is present and a ï¿½0ï¿½ means it is not present.

The different parts of a computer communicate through pulses of current (1s and 0s). As we all know, computers can calculate complex equations and perform complex mathematics at lightening speed. Calculating using only 1s and 0s is called the BINARY SYSTEM. Although a computer will only process 1s and 0s there comes a point when the 1s and 0s have to be converted into our usual decimal numbers - that we are familiar with. We tend to use the DECIMAL SYSTEM when attempting maths. This system deals with numbers that we are using on a daily basis: 1,2,3,4,5,6,7,8,9, 10s, 100s, 1000s etc..... As the BINARY system is composed of only two numbers (1s and 0s) you may be wandering how it is possible to count beyond one. The table below will help you understand how this is done. Look at the row that represents the decimal number 10 (diagram below). The table can be used to convert this decimal number to a binary number.

The table shows that DECIMAL 10 is composed of one number 8 and one number 2. Zeros are used to fill the blank spaces which gives 1010 as the binary equivalent of decimal 10. Next look at the way decimal 60 is converted to its binary equivalent. 60 is composed of one 32, one 16, one 8, and one 4. The blanks are filled with zeros giving 111100 as the binary equivalent of decimal 60. The important point to remember is that when converting from decimal to binary OR from binary to decimal, you must write down the top section of the table (seen in yellow above) and underneath enter the binary number. QUESTIONS: 1. What do you notice about the way the numbers along the top section of the table increase - from right to left (yellow section of table)? 2. Complete the table by writing the binary equivalent of decimal numbers 44, 19, 27 and 7, in the spaces available.

How1sand0srule - HOW 1s AND 0s RULE THE WORLD Utku Altunkaya Outline How1sand0srule How1sand0srule - HOW 1s AND 0s RULE THE WORLD Utku... SCHOOL View Full Document This is the end of the preview. Sign up to access the rest of the document. Unformatted text preview: HOW 1s AND 0s RULE THE WORLD Utku Altunkaya Outline Introduction Basic Logic Operations Logic Circuits Base-2 (Binary) Number System Analog vs. Digital Signals and Systems Implementation Technologies for Digital Circuits Introduction All digital systems are built around the fundamentals of the base-2 (binary) number system, which uses only 1s and 0s to represent numbers. Anything that can be expressed as a binary number can be processed by a digital system.

Introduction Here are a few concepts and acronyms related to digital systems that are widely used in daily life: Bits, bytes, kilo-, mega-, and gigabytes Microprocessors, RAM, ROM CD-ROM, CD- Audio, MP3 compression DVD, MPEG and DivX compression Internet, modem, ADSL, kbps, mbps Logic Operations THE AND GATE The AND gate implements the Boolean AND function where the output is logic 1 only when all inputs to the AND gate are logic 1. The standard symbol and the truth table for a two-input AND gate is: The Boolean expression for the AND gate is Y = A B Logic Operations THE OR GATE The OR gate implements the Boolean OR function where the output is logic 1 when any input to the OR gate is logic 1. The standard symbol and the truth table for a two-input OR gate is: The Boolean expression for the OR gate is Y = A + B Logic Operations THE NOT GATE The NOT gate (Inverter) implements the Boolean NOT function where the output is the inverse of the input. The standard symbol and the truth table for the NOT gate is: The Boolean expression for the NOT gate is Y = A ....

Istanbul Technical University EE ee431 - Spring 2004 In the Boolean Algebra S=cfw_0,1,2,3 and f:S2S, we want to find BFs having the same v FindFunctionsWith-4CommonPoints Numbering Systems Numbering Systems as a Microsoft Word 97-98 file. Learning Objectives To understand the principles of numbering systems To convert numbers from one base to another To be able to do arithmetic in binary and hexadecimal This supplement to Long and Long learning resources (published by Prentice Hall) on computer competency presents the principles of numbering systems, discusses numbering-system arithmetic, and illustrates how to convert a value in one numbering system to its equivalent in another. After studying this supplement you will be able to perform rudimentary arithmetic operations in the binary and hexadecimal numbering systems. CONTENTS NUMBERING SYSTEMS AND COMPUTERS We humans use a decimal, or base-10, numbering system, presumably because people have 10 fingers.

If we had three fingers and a thumb on each hand, as does the Extra Terrestrial (E.T.), from the classic movie, and Homer Simpson of the Simpsons, then in all probability we would be using the octal numbering system, which has a base of 8. Early computers were designed around the decimal numbering system. This approach made the creation of computer logic capabilities unnecessarily complex and did not make efficient use of resources. (For example, 10 vacuum tubes were needed to represent one decimal digit.) In 1945, as computer pioneers were struggling to improve this cumbersome approach, John von Neumann suggested that the numbering system used by computers should take advantage of the physical characteristics of electronic circuitry. To deal with the basic electronic states of on and off, von Neumann suggested using the binary numbering system. His insight has vastly simplified the way computers handle data. Computers operate in binary and communicate to us in decimal. A special program translates decimal into binary on input, and binary into decimal on output. Under normal circumstances, a programmer would see only decimal input and output.

On occasion, though, he or she must deal with long and confusing strings of 1s and 0s that represent the content of RAM, the computers memory. Occasionally a programmer or computer engineer takes a snapshot of the contents of RAM (on-bits and off-bits) at a given moment in time. To reduce at least part of the confusion of seeing only 1s and 0s on the output, the hexadecimal (base-16) numbering system is used as a shorthand to display the binary contents of both RAM and secondary storage, such as disk. The decimal equivalents for binary, decimal, and hexadecimal numbers are shown in Figure 1. We know that in decimal, any number greater than 9 is represented by a sequence of digits. When you count in decimal, you "carry" to the next position in groups of 10. As you examine Figure 1, notice that you carry in groups of 2 in binary and in groups of 16 in hexadecimal. Also note that any combination of four binary digits can be represented by one "hex" digit.

FIGURE 1 Numbering System Equivalence Table The hexadecimal numbering system is used only for the convenience of the programmer or computer scientist, or computer engineer when reading and reviewing the binary display of memory. Computers do not operate or process in hex. During the 1960s and early 1970s, programmers often had to examine the contents of RAM to debug their programs (that is, to eliminate program errors). Today's programming languages have user friendly diagnostics (error messages) and computer-assisted tools that help programmers during program development. These diagnostics and development aids have minimized the need for applications programmers to convert binary and hexadecimal numbers into their more familiar decimal equivalents. However, if you become familiar with these numbering systems, you should achieve a better overall understanding of computers. And, someday you may need to read hex to decode an error message or set the jumpers on an expansion card. PRINCIPLES OF NUMBERING SYSTEMS Binary The binary, or base-2, numbering system is based on the same principles as the decimal, or base-10, numbering system, with which we are already familiar.

The only difference between the two numbering systems is that binary uses only two digits, 0 and 1, and the decimal numbering system uses 10 digits, 0 through 9. The equivalents for binary, decimal, and hexadecimal numbers are shown in Figure 1. The value of a given digit is determined by its relative position in a sequence of digits. Consider the example in Figure 2. If we want to write the number 124 in decimal, the interpretation is almost automatic because of our familiarity with the decimal numbering system. To illustrate the underlying concepts, let's give Ralph, a little green two-fingered Martian, a bag of 124 (decimal) marbles and ask him to express the number of marbles in decimal. Ralph, who is more familiar with binary, would go through the following thought process (see Figure 2). FIGURE 2 Numbering System Fundamentals Ralph, our two-fingered Martian who is used to counting in binary, might go through the thought process illustrated here when counting 124 marbles in decimal. Ralph's steps are discussed in the text. Step 1.

Ralph knows that the relative position of a digit within a string of digits determines its value, whether the numbering system is binary or decimal. Therefore, the first thing to do is determine the value represented by each digit position. Step 2. Ralph knows that as in any numbering system, the rightmost position has a value of the base to the zero power, or 1 (100 = 1). The second position is the base to the first power, or 10 (101 = 10). The third position is the base squared, or 100, and so on. Step 3. Because the largest of the decimal system's 10 digits is 9, the greatest number that can be represented in the rightmost position is 9 (9 X 1). The greatest number that can be represented in the second position, then, is 90 (9 X 10). In the third position, the greatest number is 900, and so on. Having placed the marbles in stacks of 10, Ralph knows immediately that there will be no need for a fourth-position digit (the thousands position).

It is apparent, however, that a digit must be placed in the third position. Because placing a 2 in the third position would be too much (200 > 124), Ralph places a 1 in the third position to represent 100 marbles. Step 4. Ralph must continue to the second position to represent the remaining 24 marbles. In each successive position, Ralph wants to represent as many marbles as possible. In this case, a 2 placed in the second position would represent 20 of the remaining marbles (2 X 101 = 20). Step 5. There are still four marbles left to be represented. This can be done by inserting a 4 in the rightmost, or "ones," position. Step 6. The combination of the three numbers in their relative positions represents 124 (decimal). Ralph would go through the same thought process if asked to represent the 124 (decimal) marbles using the binary numbering system (see Figure 3). To make the binary conversion process easier to follow, the computations in Figure 3 are done in the more familiar decimal numbering system.

See if you can trace Ralph's steps as you work through Figure 3. FIGURE 3 Representing a Binary Number To represent 124 marbles in binary, we would follow the same thought process as we would in decimal (see Figure 2), but this time we have only two digits (0 and 1). For ease of understanding, the arithmetic is done in decimal. Hexadecimal Perhaps the biggest drawback to using the binary numbering system for computer operations is that programmers may have to deal with long and confusing strings of 1s and 0s. To reduce the confusion, the hexadecimal, or base-16, numbering system is used as shorthand to display the binary contents of primary and secondary storage. Notice that the bases of the binary and hexadecimal numbering systems are multiples of 2: 2 and 24, respectively. Because of this, there is a convenient relationship between these numbering systems. The numbering-system equivalence table shown in Figure 1 illustrates that a single hexadecimal digit represents four binary digits (01112 = 716, 11012 = D16, 10102 = A16 where subscripts are used to indicate the base of the numbering system).

Notice that in hexadecimal, or "hex," letters are used to represent the six higher order digits. Two hexadecimal digits can be used to represent the eight-bit byte of an EBCDIC equals sign (=) (011111102 is the same as 7E16). Figure 4 illustrates how a string of EBCDIC bits can be reduced to a more recognizable form using hexadecimal. FIGURE 4 System Expressed in Different Ways The word System is shown as it would appear in input/output, internal binary notation, and hexadecimal notation. We will now examine how to convert one number in a numbering system to an equivalent number in another numbering system. For example, there are occasions when we might wish to convert a hexadecimal number into its binary equivalent. We shall also learn the fundamentals of numbering-system arithmetic. CONVERTING NUMBERS FROM ONE BASE INTO ANOTHER Decimal to Binary or Hexadecimal A decimal number can be converted easily into an equivalent number of any base by the use of the division/remainder technique. This two-step technique is illustrated in Figure 5. Follow these steps to convert decimal to binary.

FIGURE 5 Converting a Decimal Number into Its Binary Equivalent Use the twoBstep division/remainder technique to convert a decimal number into an equivalent number of any base. Step 1. Divide the number (19, in this example) repeatedly by 2, and record the remainder of each division. In the first division, 2 goes into 19 nine times with a remainder of 1. The remainder is always one of the binary digits--0 or 1. In the last division you divide 1 by the base (2) and the remainder is 1. Step 2. Rotate the remainders as shown in Figure 5; the result (10011) is the binary equivalent of a decimal 19. Figure 6 illustrates how the same division/remainder technique is used to convert a decimal 453 into its hexadecimal equivalent (1C5). In a decimal-to-hex conversion, the remainder is always one of the 16 hex digits. FIGURE 6 Converting a Decimal Number into Its Hexadecimal Equivalent The two-step division/remainder technique is used to convert a decimal number to its hex equivalent.

Binary to Decimal and Hexadecimal To convert from binary to decimal, multiply the 1s in a binary number by their position values, then sum the products (see Figure 7). In Figure 7, for example, binary 11010 is converted into its decimal equivalent (26). FIGURE 7 Converting a Binary Number into Its Decimal Equivalent Multiply the 1s in a binary number by their position values. The easiest conversion is binary to hex. To convert binary to hex, simply begin with the 1s position on the right and segment the binary number into groups of four digits each (see Figure 8). Refer to the equivalence table in Figure 2, and assign each group of four binary digits a hex equivalent. Combine your result, and the conversion is complete. Hexadecimal to Binary To convert hex numbers into binary, perform the grouping procedure for converting binary to hex in reverse (see Figure 8). FIGURE 8 Converting a Binary Number into Its Hexadecimal Equivalent Place the binary digits in groups of four, then convert the binary number directly to hexadecimal. Hexadecimal to Decimal Use the same procedure as that used for binary-to-decimal conversions (see Figure 7) to convert hex to decimal.

Figure 9 demonstrates the conversion of a hex 3E7 into its decimal equivalent of 999. FIGURE 9 Converting a Hexadecimal Number into Its Decimal Equivalent Multiply the digits in a hexadecimal number by their position values. ARITHMETIC IN BINARY AND HEXADECIMAL The essentials of decimal arithmetic operations have been drilled into us so that we do addition and subtraction almost by instinct. We do binary arithmetic, as well as that of other numbering systems, in the same way that we do decimal arithmetic. The only difference is that we have fewer (binary) or more (hexadecimal) digits to use. Figure 10 illustrates and compares addition and subtraction in decimal with that in binary and hex. Notice in Figure 10 that you carry to and borrow from adjacent positions, just as you do in decimal arithmetic. FIGURE 10 Binary, Decimal, and Hexadecimal Arithmetic Comparison As you can see, the only difference in doing arithmetic in the various numbering systems is the number of digits used. Binary Number System Binary Number System A Binary Number is made up of only 0s and 1s.

110100 Example of a Binary Number There is no 2, 3, 4, 5, 6, 7, 8 or 9 in Binary! A "bit" is a single binary digit. The number above has 6 bits. Binary numbers have many uses in mathematics and beyond. In fact the digital world uses binary digits . How do we Count using Binary? Binary But then there is no symbol for 2 ... what do we do? Well how do we count in Decimal? This is the last digit in Decimal So we start back at 0 again, but add 1 on the left The same thing is done in binary ... Now start back at 0 again, but add 1 on the left ••• When we run out of digits, we ... ... start back at 0 again, but add 1 on the left And that is what we do in binary ... Start back at 0 again, but add 1 on the left ••• start back at 0 again, and add one to the number on the left... ... but that number is already at 1 so it also goes back to 0 ... ...

and 1 is added to the next position on the left ••••• Start back at 0 again (for all 3 digits), add 1 on the left ••••••••• See how it is done in this little demonstration (press play button): Decimal vs Binary Here are some equivalent values: Decimal: Here are some larger equivalent values: Decimal: "Binary is as easy as 1, 10, 11." Now see how you can use Binary to count past 1,000 on your fingers: In the Decimal System there are Ones, Tens, Hundreds, etc In Binary there are Ones, Twos, Fours, etc, like this: This is 1×8 + 1×4 + 0×2 + 1 + 1×(1/2) + 0×(1/4) + 1×(1/8) = 13.625 in Decimal Numbers can be placed to the left or right of the point, to show values greater than one and less than one.

10.1 The number to the left of the point is a whole number (such as 10) As we move further left, every number place gets 2 times bigger. The first digit on the right means halves (1/2). As we move further right, every number place gets 2 times smaller (half as big). Example: 10.1 The "10" means 2 in decimal, The ".1" means half, You can do conversions at Binary to Decimal to Hexadecimal Converter . Words The word binary comes from "Bi-" meaning two. We see "bi-" in words such as "bicycle" (two wheels) or "binocular" (two eyes). When you say a binary number, pronounce each digit (example, the binary number "101" is spoken as "one zero one", or sometimes "one-oh-one"). This way people don't get confused with the decimal number. A single binary digit (like "0" or "1") is called a "bit". For example 11010 is five bits long.

The word bit is made up from the words "binary digit" How to Show that a Number is Binary To show that a number is a binary number, follow it with a little 2 like this: 1012 This way people won't think it is the decimal number "101" (one hundred and one). Examples Example: What is 11112 in Decimal? The "1" on the left is in the "2×2×2" position, so that means 1×2×2×2 (=8) The next "1" is in the "2×2" position, so that means 1×2×2 (=4) The next "1" is in the "2" position, so that means 1×2 (=2) The last "1" is in the ones position, so that means 1 Answer: 1111 = 8+4+2+1 = 15 in Decimal Example: What is 10012 in Decimal?

The "1" on the left is in the "2×2×2" position, so that means 1×2×2×2 (=8) The "0" is in the "2×2" position, so that means 0×2×2 (=0) The next "0" is in the "2" position, so that means 0×2 (=0) The last "1" is in the ones position, so that means 1 Answer: 1001 = 8+0+0+1 = 9 in Decimal Example: What is 1.12 in Decimal? The "1" on the left side is in the ones position, so that means 1. The 1 on the right side is in the "halves" position, so that means 1×(1/2) So, 1.1 is "1 and 1 half" = 1.5 in Decimal Example: What is 10.112 in Decimal?

The "1" is in the "2" position, so that means 1×2 (=2) The "0" is in the ones position, so that means 0 The "1" on the right of the point is in the "halves" position, so that means 1×(1/2) The last "1" on the right side is in the "quarters" position, so that means 1×(1/4) So, 10.11 is 2+0+1/2+1/4 = 2.75 in Decimal "There are 10 kinds of people in the world, those who understand binary numbers, and those who don't." Chapter 4 - The Component of the System Unit Identify components in a handheld computer Chapter 4 presented the components in the system unit, described how memory stores data, instructions, and information, and discussed the sequence of operations that occur when a computer executes an instruction. The chapter included a comparison of various microprocessors on the market today. Describe the components in the system unit The system unit, sometimes called the chassis, is a box-like case housing the electronic components of a computer that are used to process data.

System unit components include the processor, memory module, cards, ports, and connectors. Many of the system unitï¿½s components reside on a circuit board called the motherboard. The motherboard contains many different types of chips, or small pieces of semiconducting material, on which one or more integrated circuits (IC) are etched. An integrated circuit is a microscopic pathway capable of carrying electronic current. Each IC can contain millions of transistors, which act as switches for electronic signals. Explain how the CPU uses the four steps of a machine cycle to process data The central processing unit (CPU), also called a processor, significantly impacts overall computing power and manages most of a computerï¿½s operations. The CPU contains the control unit and the arithmetic/logic unit. The control unit directs and coordinates most of the operations in the computer. For every instruction, the control unit repeats a set of four basic operations called the machine cycle: (1) fetching the instruction or data item from memory, (2) decoding the instruction into commands the computer understands, (3) executing the commands, and, if necessary, (4) storing, or writing the result to memory.

The arithmetic/logic unit (ALU) performs the execution part of the machine cycle. Specifically, the ALU carries out three operations: Arithmetic operations ï¿½ performing calculations, which include addition, subtraction, multiplication, and division Comparison operations ï¿½ comparing data items to determine if the first item is greater than, equal to, or less than the other item Logical operations ï¿½ working with conditions and logical operators such as AND, OR, and not Compare and contrast various personal computer processors on the market today A personal computerï¿½s CPU usually is contained on a single chip, which some call a microprocessor. Intel is a leading manufacturer of personal computer processors. Most high-performance PCs use a processor from Intel called the Pentiumï¿½ processor. A second Intel brand, called the Celeronï¿½, is designed for less expensive PCs. Two more brands, called the Xeonï¿½ and Itaniumï¿½ processors, are ideal for workstations and low-end servers. Intel-compatible processors have the same internal design as Intel processors and perform the same functions, but are made by other companies and often are less expensive.

An alternative design to the Intel-style processor, the Motorola processor, is found in Apple Macintosh and Power Macintosh systems. A new type of processor designed for lower-costing personal computers and Internet appliances, called an integrated CPU, combines functions of a processor, memory, and a video card on a single chip. Todayï¿½s processors are equipped with MMXï¿½ technology, a built-in set of instructions that manipulates and processes multimedia data more efficiently. Intelï¿½s SSE instructions and AMDï¿½s 3DNow!ï¿½ are two other technologies that improve a processorï¿½s performance of multimedia, the Web, and 3-D graphics. To optimize and extend battery life for notebook computers, Intelï¿½ mobile processors use SpeedStepï¿½ technology and AMD processors use PowerNow!ï¿½ technology. Define a bit and describe how a series of bits represents data Most computers are digital, meaning they understand only two discrete states: on and off. These states are represented using two digits, 0 (off) and 1 (on). Each on or off value is called a bit (short for binary digit), the smallest unit of data a computer can handle.

Eight bits grouped together as a unit form a byte. A byte provides enough different combinations of 0s and 1s to represent 256 individual characters including numbers, letters of the alphabet, punctuation marks, and other characters. The combinations of 0s and 1s used to represent data are defined by patterns called coding schemes. Popular coding schemes are ASCII, EBCDIC, and Unicode. Coding schemes make it possible for humans to interact with a digital computer that recognizes only bits. Every character you type on a keyboard is converted into a corresponding byte, a series of on/off electrical states the computer can process. Differentiate between the various types of memory Memory is a temporary storage place for data, instructions, and information. Memory stores the operating system, application programs, and the data processed by application programs. A byte is the basic storage unit in memory. Memory size is measured by the number of bytes available for use. A kilobyte (KB or K) of memory is approximately one thousand bytes, a megabyte (MB) is approximately one million bytes, and a gigabyte (GB) is approximately one billion bytes. The system unit contains several types of memory.

RAM (random access memory) consists of memory chips that the processor can read from and write to. Most RAM is volatile memory, meaning that its contents are lost when the computerï¿½s power is turned off. Two basic types of RAM chips are dynamic RAM and static RAM. Dynamic RAM (DRAM) must be re-energized constantly or it loses its contents. Static RAM (SRAM) is faster and more reliable than DRAM and has to be re-energized less often, but it is much more expensive. Memory cache, also called a cache store or RAM cache, improves processing time by storing frequently used instructions and data. ROM (read-only memory) refers to memory chips that only can be read and used; that is, they cannot be modified. ROM is nonvolatile memory (NVM), meaning that its contents are not lost when the computerï¿½s power is turned off. A variation of the ROM chip, called programmable read-only memory (PROM), is a blank chip on which you can place items permanently. Flash memory, also known as flash ROM or flash RAM, is nonvolatile memory that can be erased electronically and reprogrammed.

Complementary metal-oxide semiconductor (CMOS) memory, another type of memory chip, stores configuration information about the computer and uses battery power to retain information when the power to the computer is off. Describe the types of expansion slots and cards in the system unit An expansion slot is an opening, or socket, where you can insert a circuit board into the motherboard. These circuit boards ï¿½ called cards, expansion cards, boards, expansion boards, adapters, adapter cards, interface cards, add-ins, or add-ons -- add new devices or capabilities to the computer. Four types of expansion cards found in most computers are a video card, a sound card, a network interface card, and a modem card. A video card converts computer output into a video signal that is sent through a cable to the monitor, which displays an image. A sound card enhances the sound-generating capabilities of a personal computer by allowing sound to be input through a microphone and output through speakers. A network interface card (NIC) is a communications device that allows the computer to communicate via a network. A modem card is a communications device that enables computers to communicate via telephone lines or other means.

Many of todayï¿½s computers support Plug and Play, a capability with which the computer automatically can configure expansion boards and other devices as you install them. Notebook and other portable computers have a special type of expansion slot used for installing a PC Card, which is a thin credit card-sized device that adds memory, disk drives, sound, fax/modem, and communications capabilities to a mobile computer. Explain the difference between a serial, a parallel, and a USB port A cable often attaches external devices to the system unit. A port is the interface, or point of attachment, to the system unit. Ports have different types of connectors, which are used to join a cable to a device. Male connectors have one or more exposed pins, while female connectors have matching holes to accept the pins. Most computers have three types of ports: serial, parallel, and USB. A serial port is a type of interface that connects a device to the system unit by transmitting data only one bit at a time. Serial ports usually connect devices that do not require fast data transmission rates, such as a mouse, keyboard, or modem. A parallel port is an interface that connects devices by transferring more than one bit at a time.

Many printers connect to the system unit using a parallel port. A universal serial bus (USB) port can connect up to 127 different peripheral devices with a single connector type, greatly simplifying the process of attaching devices to a personal computer. Describe how buses contribute to a computer's processing speed Bits are transferred internally within the circuitry of the computer along electrical channels. Each channel, called a bus, allows various devices inside and attached to the system unit to communicate with each other. The bus width, or size of the bus, determines the number of bits that can be transferred at one time. The larger the bus width, the fewer number of transfer steps required and the faster the transfer of data. In most computers word size (the number of bits the CPU can process at a given time) is the same as the bus width. Every bus also has a clock speed. The higher the bus clock speed, the faster the transmission of data, which results in applications running faster. A computer has two basic types of buses. A system bus connects the CPU to main memory. An expansion bus allows the CPU to communicate with peripheral devices.

Identify components in a notebook computer Users with mobile computing needs often have a mobile computer, such as a notebook computer and/or handheld computer. A notebook computer, also called a laptop computer, can run either using batteries or using a standard power supply. In addition to the motherboard, processor, memory, sound card, PC Card slot, and drive bay, the system unit for a notebook computer also houses other devices, such as the keyboard, pointing device, speakers, and display. Identify components in a handheld computer Handheld computers run strictly on battery. Similar to desktop and notebook computers, handheld computers have a system unit that contains electronic components that process data. A handheld computerï¿½s system unit also contains a display and may house speakers and some form of keyboard and/or pointing device. Handheld computers often have an IrDA port so you can communicate wirelessly with other computers. Many also include a serial port. The motherboard in the system unit contains different types of chips. Manufacturers package chips so the chips can be attached to circuit boards, such as the motherboard.

Types of chip packages include: Dual inline package (DIP), which consists of two parallel rows of downward-pointing thin metal feet (pins) Pin grid array (PGA) package, which holds a larger number of pins because the pins are mounted on the surface of the package Flip chip-PGA (FC-PGA) package, which places chips on the opposite side (flip side) of the pins Single edge contact (SEC) cartridge, which connects to the motherboard on one of its edges The CPU The power of personal computer processor chips (the chips that contain the CPU) has grown at an astounding rate. As chips become older and more widely used, price cuts usually are introduced. Several factors affect CPU processing speed. CPUs in most of todayï¿½s personal computers use pipelining, a technique that increases processing speed by beginning execution of a second machine cycle instruction before the first instruction is completed. CPUs also use high-speed storage locations, called registers, to hold data and instructions temporarily. The control unit relies on a small chip called the system clock to synchronize all computer operations. The speed at which a processor executes instructions is called clock speed, or clock rate, and is measured in megahertz (MHz).

The system clock is a major factor affecting processor speed. A higher clock speed means the CPU can process more instructions per second. Processor Comparison Although once frequently used, the term ï¿½microprocessorï¿½ is much less common today. Sometimes you can upgrade your processor to increase the computerï¿½s performance. There are three forms of upgrades: With a chip for chip upgrade, the existing processor chip is replaced with a new one With a piggyback upgrade, the new processor is stacked on top of the old one With a daughterboard upgrade, the new processor is on a small circuit board (the daughterboard) that plugs into the motherboard The past three years have seen a steady drop in the cost of computers. PC prices plunged as a result of lower prices for processors, memory chips, and hard drives. Consumers also are showing increased interest in new less powerful, but less expensive, personal computers that work perfectly well for the most popular uses ï¿½ word processing, Internet access, and spreadsheet applications. The surge in low-priced computer sales has had an impact on Intel, the worldï¿½s largest processor manufacturer. By focusing on making inexpensive processor chips, rivals AMD and Cyrix are making inroads into Intelï¿½s dominance.

Intelï¿½s response, the Celeronï¿½, has proven popular, but the lower-priced chip offers a smaller profit margin. Data Representation Just as the decimal system (10 digits) is suited to human anatomy (10 fingers), the binary system (2 digits) is perfect to represent the on-off states (2 states) of a computer. Basic coding standards make it possible for components within computers to communicate, allow manufacturers to be confident that the components they produce will operate correctly in a computer, and enable consumers to purchase components that are compatible with their systems. In the ASCII-8 and EBCDIC codes, the first four characters represent the zone, and the last four characters represent the digits 1 through 8. ASCII, originally a seven-bit code, was expanded to eight bits in an effort to provide for symbols used in other nations. Unicode, a 2-byte (16-bit) code, can represent 216, or 65,536, characters.

The system employs the codes used by ASCII and also includes other alphabets (such as Cyrillic and Hebrew), special characters (including religious symbols), and some of the ï¿½word writingï¿½ symbols used by various Asian countries. Memory Because computers use the binary number system, the actual values for the units in which memory and storage are measured are based on powers of 2. For example, one kilobyte = 210 = 1,024. RAMï¿½s volatility, and its ability to be changed, are its most distinguishing characteristics. When RAM is purchased it comes in banks of nine chips ï¿½ eight are needed to represent a byte and the ninth is needed for parity. RAM chips usually are packaged on small circuit boards called single inline memory modules (SIMMs) or dual inline memory modules (DIMMs) that are inserted into the motherboard. During the past 20 years, the price of RAM has dropped an average of 20 percent each year, but its capacity has more than doubled every two years. Similar to flash ROM, another variation of ROM, called EEPROM (electrically erasable programmable read-only memory), can be erased electrically and rewritten.

Because of its nonvolatile nature, EEPROM is used in electronic cash registers to store item prices. The amount of time it takes the processor to read data from memory, called access time, directly affects how fast the computer can process data. Memory access time is measured in terms of nanoseconds, or billionths of a second. Expansion Slots and Expansion Cards Plug and Play was a much-touted feature of the Windows 95 and Windows 98 operating systems. A PC Card slot, usually located on the side of a notebook computer, allows a PC Card to be changed without having to open the system unit. There are three types of PC Cards: Type I cards add memory capabilities to the computer Type II cards contain communications devices Type III cards house devices such as hard disks Ports Port connectors are devised to be foolproof ï¿½ each is designed so it can fit only one type of socket in only one correct position. Serial ports always are male on the system case. Cables connected to parallel ports often are employed over shorter distances.

Special-purpose ports include: 1394 port ï¿½ a port that can connect multiple devices requiring faster data transmission speeds such as digital cameras and DVD drives MIDI (musical instrumental digital interface) port ï¿½ a special type of serial port designed to connect the system unit to a musical instrument SCSI (small computer system interface) port ï¿½ a high-speed parallel port used to attach peripheral devices such as disk drives and printers IrDA port ï¿½ a port that allows wireless devices to transmit signals to a computer via infrared light waves Buses A highway analogy can help clarify how bus width affects the speed of data transfer. Data moves like cars ï¿½ the more lanes (greater the bus width) the faster the traffic (data) flow. Ideally, buses used to transfer data should be large enough to use the processing power of registers. Sometimes, however, manufacturers reduce bus size to cut costs. Word size, which indicates the number of bits processed in each machine cycle, has been compared to the amount of coffee produced with each turn of a coffee grinderï¿½s handle. Theoretically, if word size doubles then processor throughput also could double.

The types of expansion buses on a motherboard determine the types of cards you can add to a computer. Types of expansion buses include: An ISA (Industry Standard Architecture) bus, the most common and slowest expansion bus, connects to devices such as a mouse, modem card, sound card, and low-speed network card A local bus is a high-speed expansion bus used to connect higher speed devices such as hard disks An Accelerated Graphics Port (AGP) is a bus designed by Intel to improve the speed with which 3-D graphics and video transmit The universal serial bus (USB) and 1394 bus are buses that eliminate the need to install expansion cards into expansion slots A PC Card bus is the expansion bus for a PC Card Notebook Computers A typical notebook computer often has a keyboard/mouse, IrDA, serial, parallel, video, and USB ports. The keyboard/mouse port allows users who are uncomfortable with a notebook computerï¿½s smaller keyboard and less-traditional pointing devices (often a touch pad or pointing stick) to connect a full-sized keyboard or a mouse to the computer. Handheld Computers One of the most popular handheld computers is the Palm Pilot from 3Com.

First introduced in 1996, a recent version, Palm IIIc, offers a color screen and an expandable, full-sized keyboard. Another pioneering handheld computer is Visor from Handspring. Visor runs the Palm operating system and features an expansion slot that can accommodate add-ons such as digital cameras and music players. Visorï¿½s greatest innovation, however, may be the slot in the back, which can accommodate modules with various functions including a pager, an MP3 music player, videogame cartridges, and a module that converts the Visor into a cell telephone.

Question: What number system uses only 0's and 1's?
Answer: Binary