Patent Publication Number: US-6223199-B1

Title: Method and apparatus for an N-NARY HPG gate

Description:
This application claims the benefits of the earlier filed U.S. Provisional Application Ser. No. 60/069250, filed Dec. 11, 1997, which is incorporated by reference for all purposes into this application. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to digital computing, and more particularly to an apparatus and method for implementing carry-lookahead circuitry using 1-of-N logic. 
     2. Description of the Related Art 
     Traditional Binary Addition 
     In most computer systems, addition and subtraction of numbers is supported. In systems using traditional binary logic, the truth table for one-bit addition is set forth in Table 1. 
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 A 
                 B 
                 A + B 
               
               
                   
                   
               
             
            
               
                   
                 0 
                 0 
                 0 
               
               
                   
                 0 
                 1 
                 1 
               
               
                   
                 1 
                 0 
                 1 
               
               
                   
                 1 
                 1 
                 0* 
               
               
                   
                   
               
            
           
         
       
     
     In the last row of Table 1, a carry condition occurs. That is, the result is 0, but a carry into the next-higher-order bit position, corresponding to a decimal value of 2, has conceptually occurred. 
     In addition to single bits, the addition operation may be performed on multiple bits, including addition of two two-bit values. The truth table for such an operation is set forth in Table 2, where the first operand A is a two-bit value comprising bits A 0  and A 1 . The second operand, B, is a two-bit value comprising bits B 0  and B 1 . 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                   
                   
                 A = 
                 B = 
                   
                 A + B = 
               
               
                   
                   
                   
                   
                 Decimal 
                 Decimal 
                   
                 Dec. 
               
               
                 A 1   
                 A 0   
                 B 1   
                 B 0   
                 Value 
                 Value 
                 A + B 
                 Value 
               
               
                   
               
             
            
               
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 00 
                 0 
               
               
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 01 
                 1 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 2 
                 10 
                 2 
               
               
                 0 
                 0 
                 1 
                 1 
                 0 
                 3 
                 11 
                 3 
               
               
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 01 
                 1 
               
               
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
                 10 
                 2 
               
               
                 0 
                 1 
                 1 
                 0 
                 1 
                 2 
                 11 
                 3 
               
               
                 0 
                 1 
                 1 
                 1 
                 1 
                 3 
                 00* 
                 0 
               
               
                 1 
                 0 
                 0 
                 0 
                 2 
                 0 
                 10 
                 2 
               
               
                 1 
                 0 
                 0 
                 1 
                 2 
                 1 
                 11 
                 3 
               
               
                 1 
                 0 
                 1 
                 0 
                 2 
                 2 
                 00* 
                 0 
               
               
                 1 
                 0 
                 1 
                 1 
                 2 
                 3 
                 01* 
                 1 
               
               
                 1 
                 1 
                 0 
                 0 
                 3 
                 0 
                 11 
                 3 
               
               
                 1 
                 1 
                 0 
                 1 
                 3 
                 1 
                 00* 
                 0 
               
               
                 1 
                 1 
                 1 
                 0 
                 3 
                 2 
                 01* 
                 1 
               
               
                 1 
                 1 
                 1 
                 1 
                 3 
                 3 
                 10* 
                 2 
               
               
                   
               
            
           
         
       
     
     Each output value in the “A+B” column of Table 2 indicated with an asterisk denotes a carry condition where a one has conceptually carried into the next-higher-order bit (the bit position corresponding to a decimal value of four). 
     N-NARY Logic 
     The present invention utilizes N-NARY logic. The N-NARY logic family supports a variety of signal encodings, including 1-of-4. The N-NARY logic family is described in a copending patent application, U.S. patent application Ser. No. 09/019,355, filed Feb. 5, 1998, now U.S. Pat. No. 6,066,965, and titled “Method and Apparatus for a N-NARY logic Circuit Using 1-of-4 Encoding”, which is incorporated herein for all purposes and hereinafter referred to as “The N-NARY Patent.” In 1-of-4 encoding, four wires are used to indicate one of four possible values. In contrast, traditional static design uses two wires to indicate four values, as is demonstrated in Table 2. In Table 2, the A 0  and A 1  wires are used to indicate the four possible values for operand A: 00, 01, 10, and 11. The two B wires are similarly used to indicate the same four possible values for operand B. “Traditional” dual-rail dynamic logic also uses four wires to represent two bits, but the dual-rail scheme always requires two wires to be asserted. In contrast, N-NARY logic only requires assertion of one wire. The benefits of N-NARY logic over dual-rail logic, such as reduced power and reduced noise, should be apparent from a reading of The N-NARY Patent. 
     All signals in N-NARY logic, including 1-of-4, are of the 1-of-N form where N is any integer greater than one. A 1 -of-4 signal requires four wires to encode four values (0-3 inclusive), or the equivalent of two bits of information. More than one wire will never be asserted for a 1-of-N signal. Similarly, N-NARY logic requires that a high voltage be asserted for all values, even 0. As illustrated in this specification and more thoroughly discussed in the N-NARY Patent, a 1 of N signal is used to convey multiple values of information in an integrated circuit. The 1 of N signal can convey information to and from an N-NARY logic circuit where an N-NARY logic circuit comprises a shared logic tree circuit that evaluates one or more 1 of N input signals and produces a 1 of N output signal. A single 1 of N signal comprises a bundle of N wires routed together between different cells (or different logic circuits) within a semiconductor device. A 1 of N signal uses a 1 of N encoding to indicate multiple values of information conveyed by the bundle of wires of the 1 of N signal where at most one and only one wire of the bundle of wires of the 1 of N signal is true during an evaluation cycle. The present invention further provides that the bundle of N wires may comprise a number of wires from the following group: a bundle of 3 wires, a bundle of 4 wires, a bundle of 8 wires, or a bundle of N wires. Additionally, the present invention may comprise a not valid value where zero wires of the bundle of N wires is active. Further, the present invention provides that the 1 of N encoding on the bundle of N wires cooperatively operate to reduce the power consumption in the integrated circuit according to the number of wires in the bundle of N wires evaluating per bit of encoded information. 
     Any one N-NARY gate may comprise multiple inputs and/or outputs. In such a case, a variety of different N-NARY encodings may be employed. For instance, consider a gate that comprises two inputs and two outputs, where the inputs are a 1 -of-4 signal and a 1-of-2 signal and the outputs comprise a 1-of-4 signal and a 1-of-3 signal. Various variables, including P, Q, R, and S, may be used to describe the encoding for these inputs and outputs. One may say that one input comprises 1-of-P encoding and the other comprises 1-of-Q encoding, wherein P equals two and Q equals four. Similarly, the variables R and S may be used to describe the outputs. One might say that one output comprises 1 -of-R encoding and the other output comprises 1-of-S encoding, wherein R equals four and S equals 3. Through the use of these, and other, additional variables, it is possible to describe multiple N-NARY signals that comprise a variety of different encodings. 
     SUMMARY OF THE INVENTION 
     The present invention discloses an apparatus and method for performing carry propagate logic on two 1 -of-N addends to produce a 1 -of-N carry propagate indicator. The invention comprises an HPG circuit that receives two addends and performs logic to determine whether a (P)ropagate, (H)alt, or (G)enerate signal should be set. In the preferred embodiment, the two addends and the sum comprise two-bit 1 -of-4 logic signals, and the HPG signal comprises a 1 -of-3 logic signal. The preferred embodiment of the present invention will set an H indicator for a given dit n if the sum of A n  and B n  is less than or equal to two, will set a P indicator if the sum is three, and will set a G indicator if the sum is greater than three. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of an N-NARY gate. 
     FIG. 2 is an illustration of an N-NARY adder gate. 
     FIG. 3 is a diagram of a first embodiment of an N-NARY output driver circuit. 
     FIG. 4 is a diagram of a second embodiment of an N-NARY output driver circuit. 
     FIG. 5 is a shorthand representation of an N-NARY adder gate. 
     FIG. 6 is a high-level shorthand representation of an N-NARY adder gate. 
     FIG. 7 is a shorthand representation of an N-NARY HPG gate having two 1-of-4 inputs. 
     FIG. 7A is a shorthand representation of an N-NARY HPG gate having one 1-of-3 input and one 1-of-5 input. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention relates to a Halt-Propagate-Generate (HPG) gate using N-NARY logic. This disclosure describes numerous specific details that include specific formats, structures, circuits, and logic functions in order to provide a thorough understanding of the present invention. One skilled in the art will appreciate that one may practice the present invention without these specific details. Additionally, this disclosure does not describe in detail some well-known structures such as N-FETs, P-FETs, nor does it describe N-NARY logic in detail, in order not to obscure the present invention. 
     A truth table demonstrating the add operation using 1 -of-4 encoding is set forth in Table 3. Each of the inputs A and B in Table 3 is a two-bit input that can represent one of four values, 0 through 3 inclusive, depending on which of the four wires for each signal is set high. Table 3 discards any potential input value that includes more than one wire asserted for each 1 -of-4 signal, such as 1111 and 0101. Such values are undefined for the evaluate stage of 1 -of-4 logic gates. The four wires for the two-bit sum of the 1-of-4 addition operation in Table 3 are labeled S 3 , S 2 , S 1 , and S 0 . 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                   
                   
                   
                   
                 A 
                   
                   
                   
                   
                 B 
                   
                   
                   
                   
                 Output 
               
               
                   
                   
                   
                   
                 Dec. 
                   
                   
                   
                   
                 Dec. 
                   
                   
                   
                   
                 Decimal 
               
               
                 A 3   
                 A 2   
                 A 1   
                 A 0   
                 Value 
                 B 3   
                 B 2   
                 B 1   
                 B 0   
                 Value 
                 S 3   
                 S 2   
                 S 1   
                 S 0   
                 Value 
               
               
                   
               
             
            
               
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
               
               
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
               
               
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 2 
                 0 
                 1 
                 0 
                 0 
                 2 
               
               
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 3 
                 1 
                 0 
                 0 
                 0 
                 3 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 2 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 2 
                 1 
                 0 
                 0 
                 0 
                 3 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 3 
                 0 
                 0 
                 0 
                 1 
                 0* 
               
               
                 0 
                 1 
                 0 
                 0 
                 2 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 2 
               
               
                 0 
                 1 
                 0 
                 0 
                 2 
                 0 
                 0 
                 1 
                 0 
                 1 
                 1 
                 0 
                 0 
                 0 
                 3 
               
               
                 0 
                 1 
                 0 
                 0 
                 2 
                 0 
                 1 
                 0 
                 0 
                 2 
                 0 
                 0 
                 0 
                 1 
                 0* 
               
               
                 0 
                 1 
                 0 
                 0 
                 2 
                 1 
                 0 
                 0 
                 0 
                 3 
                 0 
                 0 
                 1 
                 0 
                 1* 
               
               
                 1 
                 0 
                 0 
                 0 
                 3 
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 3 
               
               
                 1 
                 0 
                 0 
                 0 
                 3 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0* 
               
               
                 1 
                 0 
                 0 
                 0 
                 3 
                 0 
                 1 
                 0 
                 0 
                 2 
                 0 
                 0 
                 1 
                 0 
                 1* 
               
               
                 1 
                 0 
                 0 
                 0 
                 3 
                 1 
                 0 
                 0 
                 0 
                 3 
                 0 
                 1 
                 0 
                 0 
                 2* 
               
               
                   
               
            
           
         
       
     
     In Table 3, output values with asterisks indicate that a carry is conceptually generated into a higher-order bit representing a decimal value of 4. 
     N-NARY Logic Circuits 
     A background discussion of N-NARY circuits is in order before discussing the HPG gate of the present invention. N-NARY logic may be used to create circuits to perform a desired function. The present invention utilizes N-NARY logic. FIG. 1 illustrates a 1-of-N logic gate  60  that uses two sets of 1-of-N signals for the inputs and produces one 1 -of-N signal for the output. In gate  60 , the A and B inputs comprise four wires each, with each set of wires representing 2 bits (one dit) of data. A is a one-dit input, B is a one-dit input, and O is a one-dit output. In other words, the N-NARY gate  60  depicted in FIG. 1 comprises 4 input bits (2 dits) and 2 output bits (one dit). 
     Referring to FIG. 1, each N-NARY dit logic circuit  60  comprises a logic tree circuit  61 , a precharge circuit  31 , and an evaluate circuit  36 . The logic tree circuit  61  performs a logic function on the two 1 -of-4 input signals that could comprise a variety of functions, for example, the Boolean logic functions AND/NAND and OR/NOR, or the more complex carry-lookahead function of the present invention. The logic gates of the N-NARY family are clocked pre-charge (CP) gates. FIG. 2 illustrates that each input into the logic tree circuit  61  is coupled to at least one single N-channel field effect transistor (NFET) A 0 -A 3 , B 0 -B 3 . Referring back to FIG. 1, the logic tree circuit  61  therefore comprises one or more N-channel FETS. Coupled to the wires of the 1 -of-4 output signal are the output buffers  34  that aid in driving additional circuits that couple to the output signal. The preferred embodiment of the present invention uses a circuit with an inverting function as the output buffer  34 . 
     Referring again to FIG. 1, a precharge circuit  31  couples to the logic tree circuit  61  and precharges the dynamic logic of the logic tree circuit  61 . The precharge circuit  31  comprises one or more FETs with the preferred embodiment of the circuit comprising P-channel FETs (PFETs). Each evaluation path of the logic tree circuit  61  has its own precharge PFET, shown as  500  in FIG.  2 . The PFETs  500  of the precharge circuit  31  quickly and fully precharge all of the dynamic logic in the logic tree circuit  61  during the precharge phase of the clock cycle. 
     FIG. 2 is a diagram of an N-NARY adder gate. FIG. 2 illustrates that the precharge PFET  500  for an evaluation node E of an N-NARY circuit is connected to positive high voltage, Vcc, and is used to create conductive paths between the evaluation node E and Vcc. Each precharge PFET  500  is coupled to an input, the pre-charge signal. When the pre-charge signal for any evaluate node has a low voltage, then there is a conductive path between Vcc and the evaluation node E. Coupled to the precharge circuit  31  is the clock signal CK. A low clock signal on CK will cause the FETs in the logic tree circuit  32  to charge when using P-channel FETs in the precharge circuit  31 . 
     An evaluate circuit  36  couples to the logic tree circuit  61  and controls the evaluation of the logic tree circuit  61 . The evaluate circuit  36  comprises one or more FETs connected to the CK signal, with the preferred embodiment of the evaluate circuit comprising a single N-channel FET. The single N-FET acts as an evaluation transistor that is used to control when the gate is sensitive to inputs, helps avoid races between other devices, and prevents excessive power consumption. During the precharge phase, the evaluate circuit  36  receives a low value so that no path to Vss may exist through the NFET(s) of the logic tree circuit  61 . During the evaluate phase, the evaluate circuit  36  receives a high signal so that a path to Vss through the NFET(s) of the logic tree circuit  61  may exist. Coupled to the evaluate circuit  36  is the clock signal CK. A high clock signal on CK will cause the FETs in the logic tree circuit  61  to evaluate when using N-channel FETs in the evaluate circuit  36 . In other words, when the clock signal is high, the evaluate circuit  36  evaluates the logic tree circuit  61 . 
     An evaluate node, E, which comprises the four wires E 0 , E 1 , E 2 , and E 3 , is the signal pathway between the logic tree circuit  61  and an output buffer  34 , and constitutes an evaluation path of the logic tree circuit  61 . As stated earlier, each evaluation node wire E 0 , E 1 , E 2 , and E 3  has its own precharge PFET. The signal on a particular wire, E 0 , E 1 , E 2 , E 3  of the evaluate node E is high, only when there is no connection to Vss through the logic tree circuit  61  NFET(s) associated with that particular wire. If the pre-charge signal is low at time  0 , and there is no path to ground through the NFET(s) associated with an evaluate node E, of the logic tree circuit  61 , then the evaluate node wire E gets pulled to a high voltage. This is called the precharge phase of the gate and we may also say that the gate is in precharge mode. If the precharge signal switches to a high voltage at a later time, the evaluate node E will be floating but the charge left on it will leave the voltage high. This is called the evaluate phase of the gate, and we may also say that the gate is in evaluate mode. If input signals generate a high voltage for any NFET(s) in the logic tree circuit  61  such that a path from the evaluate node E to ground (Vss) exists, then the charge on the evaluate node E will drain to ground, and the evaluate voltage will drop to Vss. If no such path exists, then the evaluate node E will remain at Vcc. When any gate, therefore, switches from precharge mode to evaluate mode, the evaluate node voltage is high, and it either stays high or goes low. Once the evaluate node voltage goes low during the evaluate phase, it cannot be driven high again until the next precharge phase. 
     Each evaluate node wire E 0 , E 1 , E 2 , and E 3  couples to an output buffer  34 . Two embodiments of the output driver circuit  600  comprising output buffer  34  are illustrated in FIGS. 3 and 4. FIG. 3 illustrates a half keeper output driver circuit  602  that comprises an inverter  620  and a PFET device  640 . FIG. 4 illustrates a full keeper output driver circuit  601  that comprises an inverter  610  coupled to a PFET device  630  and an NFET device  650 . Full keeper output driver circuits  601  are only necessary for gates that can be in neither evaluate nor precharge mode for lengthy periods. The flow through the output driver circuit  600  is from evaluate node E to the output signal path O. The inverter  610 ,  620  of the output driver circuit  600  is necessary because the evaluate nodes of CP gates of the N-NARY logic family precharge to a high value and evaluate to a low value. The output driver circuit  34 , holds the value during an evaluate phase if the evaluate node E has not discharged. If the evaluate node E has discharged, then there is a path to ground holding its value low. The output of each evaluate node E will switch from low to high once, at most, during an evaluate phase. The output of each evaluate node E, once coupled to an output driver circuit  600  of output buffer  34 , is therefore suitable for feeding a subsequent CP gate. 
     A shorthand notation for circuit diagrams can be adopted to avoid needless repetition of elements common to all N-NARY circuits. FIG. 2 illustrates these common elements. One common element is the pre-charge P-FET  500 . Precharge P-FETs  500  are required for each evaluate node E in every 1 -of-N gate since a single precharge PFET  500  would short each evaluate node E relative to the other evaluate nodes. Since all N-NARY gates require a pre-charge P-FET  500  for each evaluate node E, the pre-charge P-FETs  500  may be implied and need not be shown. The same is true for the N-FET associated with each input wire of the A and B inputs. Similarly, each evaluate node E must have its own output buffer  34 , which may be implied. The N-FET associated with the evaluate node  36  may also be implied. Since these features are common to all N-NARY circuits, we may use the shorthand shown in FIG. 5 to represent the N-NARY circuits. Accordingly, FIG. 5 illustrates a shorthand notation of the adder gate depicted in FIG.  2 . This shorthand notation is used in FIGS. 5,  7 , and  7 A. In each figure, the elements discussed herein should be implied accordingly. 
     A further simplification to the representation of the FIG. 2 adder is shown in FIG. 6, where the inputs and outputs are shown as single signals that each can represent one of four signals and each impliedly comprises four wires. The number “4” shown within the add gate of FIG. 6, adjacent to the connections, indicates that each signal can represent one of four values. The number above the gate indicates the number of transistors in the evaluate stack, and the number below the FIG. 6 gate represents the maximum number of transistors in series between the evaluate node and virtual ground. In FIG. 6, the elements discussed herein should be implied accordingly. 
     Carry Propagate Logic 
     The asterisks of Table 3 illustrates that additional logic is required in order to determine whether the sum of two one-dit addends is too large to represent in two bits of information. In such cases, a carry out condition is present. What is required is a gate that can utilize carry-propagate techniques to account for carry conditions. This is accomplished through the use of carry propagate logic, as described below. 
     Carry propagate logic takes carry conditions into account. For any two binary numbers A and B, the sum, S n , and the carry, C n , for a given bit position, n, are: 
     
       
           S   n   =A   n   ⊕B   n   ⊕C   n−1 , where  C   n−1  is the carry in from the previous bit,  n −1.  (1) 
       
     
     
       
           C   n   =A   n   B   n   |A   n   C   n−1   |B   n   C   n−1 , where  C   n  is the carry out from bit n.  (2) 
       
     
     The truth tables for Equation 1 and Equation 2 are set forth in Table 4. 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                   
                   
                   
                 A n B n   
                 A n C n−1   
                 B n C n−1   
                 A n  ⊕ B n   
                 S n  = (4) ⊕ 
                 C n  = 
               
               
                 A n   
                 B n   
                 C n−1   
                 (1) 
                 (2) 
                 (3) 
                 (4) 
                 C n−1   
                 (1)|(2)|(3) 
               
               
                   
               
             
            
               
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
               
               
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 0 
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
                 0 
                 1 
               
               
                 1 
                 0 
                 0 
                 0 
                 0 
                 0 
                 1 
                 1 
                 0 
               
               
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
               
               
                 1 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
               
               
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
                 0 
                 1 
                 1 
               
               
                   
               
            
           
         
       
     
     In formulating carry propagate logic, one must recognize that the critical path in any adder is along the carry chain. The most significant bit of the sum depends not only on the two most significant addend bits, but also the addend bits of every other bit position via the carry chain. Simply allowing carries to ripple from the least significant end would result in a compact but very slow adder, since the worst-case carry propagation delay would be approximately as many gate delays as the bit width of the adder. 
     Fast carry-propagate techniques can dramatically decrease the carry propagation delay, and therefore decrease the overall delay of the adder. Adders employing such techniques are sometimes referred to as carry-lookahead adders, or CLAs. Conventional carry propagate adder structures speed up the carry chain by computing the individual carry propagate (P) and carry generate (G) signals for each bit position. 
     For any two binary numbers A and B, the P and G signals for a given bit position, n, are: 
     
       
           P   n   =A   n   ⊕B   n   (3) 
       
     
     
       
           G   n   =A   n   B   n   (4) 
       
     
     P and G may also be generated for 1 -of-4 numbers. G indicates that the given dit position, n, generates a carry that will have to be accounted for in the higher dits of the sum. G will be set when the sum of two 1-of-4 numbers is greater than 3. P indicates that any carry generated in lower dits will propagate across the given dit position, n, to affect the higher dits of the sum. P will be set when the sum of two 1-of-4 numbers is exactly three. If neither G nor P is true for a given dit position, then a carry halt signal (H) is implied. An H signal indicates that any carry generated in lower dits will not propagate across the given bit position, n. H will be set if the sum of two 1-of-4 numbers is less than three. Restated, if the sum of two operand dits in a given dit position is greater than 3, G is true. If the sum is exactly 3, P is true. Otherwise, H is true. 
     FIG. 7 illustrates an N-NARY HPG gate  700  that utilizes carry propagate logic to generate an H, P, or G indication for two 1-of-4 addends. A similar function may be performed with one 1-of-3 addend and one 1-of-5 addend. An illustration of such a gate  701  is shown in FIG.  7 A. 
     The output of the HPG gate  700  conforms to Table 5. The output of the FIG. 7 gate is a 1-of-3 N-NARY signal, such that one, and only one, of the H, P, or G wires is set high during a given evaluate cycle. The H, P, and G outputs represent the three wires for a 1-of-3 output. 
     
       
         
           
               
               
               
               
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 5 
               
               
                   
               
               
                   
                   
                   
                   
                 A Dec. 
                   
                   
                   
                   
                 B Dec. 
                   
                   
                   
               
               
                 A 3   
                 A 2   
                 A 1   
                 A 0   
                 Value 
                 B 3   
                 B 2   
                 B 1   
                 B 0   
                 Value 
                 P n   
                 G n   
                 H n   
               
               
                   
               
             
            
               
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
               
               
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
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                 1 
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                 1 
               
               
                 0 
                 0 
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                 0 
                 0 
                 1 
                 0 
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                 0 
                 0 
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                 0 
                 0 
                 0 
                 1 
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                 1 
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                 1 
                 0 
                 0 
               
               
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
                 0 
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                 0 
                 0 
                 0 
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                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 0 
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                 1 
               
               
                 0 
                 0 
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                 0 
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                 0 
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                 2 
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                 0 
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                 0 
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                 1 
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     FIG. 7 illustrates the HALT output is set high when the sum of two 1-of-4 addends equals 0, 1, or 2. The PROP output is pulled high if the sum of the addends is 3. Finally, the GEN output is pulled high when the sum of the two addends equals 4, 5, or 6. 
     In sum, the preferred embodiment of the present invention utilizes 1-of-N logic to implement a method and apparatus that perform carry propagate logic on two 1-of-N addends to produce a 1-of-3 HPG indicator that pulls the HALT wire high if the sum of the two addends is less than three, pulls the PROP wire high if the sum of the two addends is equal to three, and pulls the GEN wire high if the sum of the two addends is greater than three. 
     Other embodiments of the invention will be apparent to those skilled in the art after considering this specification or practicing the disclosed invention. The specification and examples above are exemplary only, with the true scope of the invention being indicated by the following claims.