Patent Publication Number: US-5831887-A

Title: Calculating 2A-sign(A) in a single instruction cycle

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to computer arithmetic, and more particularly to calculating the expression 2A-sign(A) for signed binary integers. 
     2. Description of Related Art 
     The Moving Picture Experts Group (MPEG) standard has emerged as the dominant standard for compressed digital video. The MPEG-1 standard specifies a compressed video bit-stream rate of approximately 1.5 megabits per second, and a compressed stereo audio bit-stream rate of approximately 250 kilobits per second. The second standard, MPEG-2, will specify compression rates for higher-bandwidth distribution media, and is in the process of being formalized. To meet the MPEG standard, video and audio compression and decompression products must rapidly process the various algorithms used to implement the MPEG standard. 
     In MPEG video signal processing, the basic video information processing unit is typically a macro-block, which has a 16×16 pixel matrix comprising four 8×8 luminance blocks, and two 8×8 chrominance blocks. Each pixel in a luminance block or chrominance block has an output corresponding to an unsigned integer number, and each macro-block is part of a much larger luminance or chrominance frame, as the case may be. 
     MPEG video signal processing includes a computation requirement for calculating sign 3 expressions such as 2A+sign(A) for each pixel in a block, where A is a signed binary integer, sign (A) is equal to one when A is greater than zero, sign(A) is equal to zero when A is zero, and sign (A) is equal to negative one when A is less than zero. For completeness, it is useful to be able to calculate other sign 3 expressions, such as 2A-sign(A). 
     FIG. 1 is a flow chart of algorithm 100, which is known, for calculating 2A-sign(A). At step 102, signed binary operand A is obtained. Decision step 104 tests whether A is zero. If A is zero, the algorithm branches to end step 116 since A provides 2A-sign(A). If A is nonzero, the algorithm branches to decision step 106 which tests whether A is negative. If A is negative, at step 108 A is added to itself to obtain 2A, at step 110 2A is incremented to obtain 2A+1, and the algorithm terminates at end step 116 since 2A+1 provides 2A-sign(A). Returning to decision step 106, if A is nonnegative (and therefore greater than zero since A is nonzero) then at step 112 A is added to itself to obtain 2A, at step 114 2A is decremented to obtain 2A-1, and the algorithm terminates at end step 116 since 2A-1 provides 2A-sign(A). Conventional variations to algorithm 100 are apparent. For instance, 2A can be calculated before determining whether 2A (and thus A) is less than, greater than or equal to zero. Although algorithm 100 and related variations are simple to implement, they normally require several instruction cycles. 
     Moreover, providing zero detect at decision step 104 may require a large amount of chip area or several instruction cycles using conventional approaches. For instance, zero detect of an n-bit operand can be provided by an n-bit OR gate coupled to an inverter. The OR gate outputs a zero, which the inverter converts to a one, only when the operand consists of zero&#39;s. Drawbacks to this approach include the increased fan-in of the OR gate, which increases chip area, and the delay associated with ORing each bit of the operand. Another known technique for zero detect of a binary operand includes serially right-shifting the operand, and inspecting the shifted-out bits one at a time. As soon as a shifted-out bit of one is detected then the operand must be nonzero, whereas if all shifted-out bits are zero&#39;s then the operand must be zero. A drawback to this approach is that the right-shifting operation can be relatively time consuming and particularly difficult to implement in a single instruction cycle. 
     Accordingly, a need exists for calculating 2A-sign(A) in a rapid and efficient manner. 
     SUMMARY OF THE INVENTION 
     An object of the invention is to provide rapid and efficient calculation of 2A-sign(A). In accordance with a preferred aspect of the invention, 2A-sign(A) is calculated by a general purpose computer in a single instruction cycle. 
     The present invention includes a method of operating a circuit to calculate 2A-sign(A). One embodiment of the method includes bit-complementing A to obtain A, bit-complementing (A-A) to obtain 2A-sign(A) when A is less than zero, bit-complementing (A+A+1) to obtain 2A-sign(A) when A is equal to zero, and bit-complementing (A+A+2) to obtain 2A-sign(A) when A is greater than zero. Preferably, the method includes setting a constant C to zero and selecting a sum output of (A+A) when A is less than zero, setting the constant C to one and selecting a sum output of (A+A+1) when A is zero, and setting the constant C to one and selecting a sum-plus-one output of (A+A+2) when A is greater than zero. Setting the constant C is in response to a sign bit of A, indicative of whether A is positive or negative, and the selecting is in response to the sign bit of A and a zero detect flag, indicative of whether A is zero or nonzero. Furthermore, zero detect of A can be provided by determining whether a first carry-out bit from (A+A+1) and a second carry-out bit from (A+A+2) have different logical values. 
     The present invention also includes an apparatus for calculating 2A-sign(A). In one embodiment, the apparatus includes first and second inverter circuits, a data selector circuit, an adder circuit, and a multiplexer in combination. The first inverter circuit provides the bit-complement of A to first and second operand inputs of the adder circuit. The data selector circuit sets a constant C to zero when A is less than zero and to one when A is greater than or equal to zero, and provides the constant C to a third operand input of the adder circuit. The adder circuit calculates (A+A) at a sum output when A is less than zero, (A+A+1) at the sum output when A is equal to zero, and (A+A+2) at a sum-plus-one output when A is greater than zero. The multiplexer selects the sum output when A is less than or equal to zero, and selects the sum-plus-one output when A is greater than zero. Finally, the second inverter circuit provides the bit-complement of the multiplexer output. Preferably, the adder circuit generates a first carry-out bit from the sum output and a second carry-out bit from the sum-plus-one output, and a zero detect circuit determines whether A is zero by determining whether the first and second carry-out bits have different logical values. 
     These and other objects, features and advantages of the invention will be further described and more readily apparent from a review of the detailed description of the preferred embodiments which follow. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the drawings, which are not necessarily drawn to scale, in which like reference characters indicate like parts: 
     FIG. 1 is a flow chart of a known algorithm for calculating 2A-sign(A). 
     FIG. 2 is a flow chart of an algorithm for calculating 2A-sign(A) in accordance with an embodiment of the present invention; 
     FIG. 3 is a block diagram of a logic circuit for calculating 2A-sign(A) in accordance with an embodiment of the present invention; 
     FIG. 4 is a block diagram of a logic circuit for calculating 2A-sign(A) in accordance with another embodiment of the present invention; and 
     FIG. 5 is a block diagram of a sum and sum-plus-one adder suitable for use in the logic circuit of FIG. 4. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The present invention calculates 2A-sign(A) in a single instruction cycle by bit-complementing A to obtain A, bit-complementing (A+A) to obtain 2A-sign(A) when A is less than zero, bit-complementing (A+A+1) to obtain 2A-sign(A) when A is equal to zero, and bit-complementing (A+A+2) to obtain 2A-sign(A) when A is greater than zero. 
     As used herein, A is a signed binary integer represented in 2&#39;s complement form. As mentioned above, sign(A) is equal to one when A is greater than zero, sign(A) is equal to zero when A is zero, and sign(A) is equal to negative one when A is less than zero. Determining whether A is positive (including zero) or negative is accomplished by inspection of its most significant bit (&#34;MSB&#34;). For a positive A the MSB=0, whereas for a negative A the MSB=1. Bit-complementing is equivalent to a 1&#39;s complement operation. For instance, A designates the bit-complement of A. Finally, incrementing refers to increasing by one. 
     The present invention is perhaps best understood by considering some of the underlying mathematics. In 2&#39;s complement representation, the negative of an integer number is provided by taking the 1&#39;s complement of the number and then incrementing, that is, 
     
         -A=A+1                                                     (1) 
    
     
         A=-A-1                                                     (2) 
    
     Consider the following algebraic manipulations for 2A-sign(A) when A is less than zero: 
     
         2A-sign(A)=2A-(-1)                                         (3) 
    
     
         2A-sign(A)=2A+2-1                                          (4) 
    
     
         2A-sign(A)=-(-2A-2)-1                                      (5) 
    
     
         2A-sign(A)=-2A-2                                           (6) 
    
     
         2A-sign(A)=(-A-1)+(-A-1)                                   (7) 
    
     
         2A-sign(A)=A+A                                             (8) 
    
     Consider the following algebraic manipulations for 2A-sign(A) when A is equal to zero: 
     
         2A-sign(A)=2A-(0)                                          (9) 
    
     
         2A-sign(A)=2A+1-1                                          (10) 
    
     
         2A-sign(A)=-(-2A-1)-1                                      (11) 
    
     
         2A-sign(A)=-2A-1                                           (12) 
    
     
         2A-sign(A)=-2A-2+1                                         (13) 
    
     
         2A-sign(A)=(-A-1)+(-A-1)+1                                 (14) 
    
     
         2A-sign(A)=A+A+1                                           (15) 
    
     Consider the following algebraic manipulations for 2A-sign(A) when A is greater than zero: 
     
         2A-sign(A)=2A-(1)                                          (16) 
    
     
         2A-sign(A)=2A+1                                            (17) 
    
     
         2A-sign(A)=-(-2A)-1                                        (18) 
    
     
         2A-sign(A)=-2A                                             (19) 
    
     
         2A-sign(A)=-2A-2+2                                         (20) 
    
     
         2A-sign(A)=(-A-1)+(-A-1)+2                                 (21) 
    
     
         2A-sign(A)=A+A+2                                           (22) 
    
     In accordance with expression (8), when A is less than zero, 2A-sign(A) is provided by bit-complementing (A+A). In accordance with expression (15), when A is equal to zero, 2A-sign(A) is provided by bit-complementing (A+A+1). In accordance with expression (22), when A is greater than zero, 2A-sign(A) is provided by bit-complementing (A+A+2). 
     FIG. 2 is a flow chart of algorithm 200 for calculating 2A-sign(A) in accordance with an embodiment of the invention. At step 202, signed binary operand A is obtained. Decision step 204 tests whether A is negative. If A is negative, at step 206 A is bit-complemented, at step 208 the sum A+A is calculated, at step 210 the sum A+A is bit-complemented to provide the result, and the algorithm terminates at end step 224. Returning to decision step 204, if A is nonnegative, at step 212 A is bit-complemented, and decision step 214 tests whether A is zero. If A is zero, at step 216 the sum A+A+1 is calculated, at step 218 the sum A+A+1 is bit-complemented to provide the result, and the algorithm terminates at end step 224. Returning to decision step 214, if A is nonzero (and therefore greater than zero since A is also nonnegative), then at step 220 the sum A+A+2 is calculated, at step 222 the sum A+A+2 is bit-complemented to provide the result, and the algorithm terminates at end step 224. 
     Variations to algorithm 200 are apparent. For instance, A can be bit-complemented before the sign bit (or complemented sign bit) of A is inspected. For each value of A, the expressions A+A, A+A+1 and A+A+2 can be calculated (concurrently if desired) with the appropriate expression selected depending on whether A is less than, equal to, or greater than zero, respectively. Likewise, A can be tested for being less than, equal to, or greater than zero before the appropriate expression is calculated. 
     Zero detect of A can be accomplished by bit-complementing A, and inspecting a carry-out bit from the MSB position generated by incrementing the bit-complement of A. The carry-out bit is a one only if the bit-complement of A is a string of one&#39;s, otherwise the carry-out bit is a zero. Furthermore, the bit-complement of A is a string of one&#39;s only if A is a string of zero&#39;s. Therefore, the carry-out bit generated by incrementing the bit-complement of A is a one only if A is zero. In a similar manner, zero detect of A can be accomplished by decrementing A, and inspecting a carry-out bit generated by incrementing A-1. 
     Zero detect of A can also be accomplished by generating a first carry-out bit from the MSB position of the sum A+A+1, generating a second carry-out bit from the MSB position of the sum A+A+2, and determining whether the first and second carry-out bits have different logical values. When A is zero, the first sum is a string of one&#39;s, the second sum is a string of zero&#39;s, and the first and second carry-out bits will have different logical values. Likewise, when A is nonzero, the first and second carry-out bits will have identical logical values. Advantageously, the first and second carry-out bits can be generated concurrently to provide rapid zero detect. Furthermore, the first and second carry-out bits can be generated without (or before) actually summing the numbers, for instance by use of PG generator sections and carry chains. 
     Zero detect of A by comparing the first and second carry-out bits is perhaps best understood by considering some of the underlying mathematics. Suppose A is an n-bit operand. If A is equal to zero, the sum A+A is an n-bit string of zero&#39;s. As a result, the bit-complement of A+A, or A+A, is an n-bit string of one&#39;s, and incrementing A+A provides an n-bit string of zero&#39;s with a carry-out bit of one. Thus, zero detect for A can be provided by adding A+A, bit-complementing A+A to obtain A+A, incrementing A+A, and inspecting the carry-out bit. In algorithm 200, however, A+A is not calculated. Consider the following algebraic manipulations: 
     
         A+A=-(A+A)-1                                               (23) 
    
     
         A+A=-A+-A-1                                                (24) 
    
     
         A+A=(A+1)+(A+1)-1                                          (25) 
    
     
         A+A=A+A+1                                                  (26) 
    
     Likewise, 
     
         A+A+1=-(A+A)-1+1                                           (27) 
    
     
         A+A+1=-A+-A-1+1                                            (28) 
    
     
         A+A+1=(A+1)+(A+1)                                          (29) 
    
     
         A+A+1=A+A+2                                                (30) 
    
     If A is an n-bit string of zero&#39;s, A+A+1 is an n-bit string of one&#39;s that generates a first carry-out bit of one from the MSB position, and A+A+2 is an n-bit string of zero&#39;s that generates a second carry-out bit of zero from the MSB position (and another carry-out bit of one from the MSB+1 position, which is discarded). Accordingly, the first and second carry-out bits have different logical values since A is zero. Remarkably, the sums A+A+1 and A+A+2 can be used for both calculating 2A-sign(A) and determining whether A is zero. 
     Further details regarding zero detect are set forth in U.S. application Ser. No. 08/658,454, filed Jun. 5, 1996, entitled &#34;Zero Detect For Binary Sum&#34; by R. Wong, which is incorporated herein by reference. 
     With regards to overflow, if A is an n-bit number, and 2A-sign(A) is an n-bit result, then overflow may occur. Overflow occurs when the MSB (or sign bit) of A and the MSB (or sign bit) of the result have different logical values. Therefore, overflow can be detected by EXCLUSIVE-ORing of the MSB of A and the MSB of the result. Furthermore, when overflow occurs, it may be desirable to clamp the result to the maximum integer value with the same sign as A. 
     Alternatively, if A is an n-bit number and 2A-sign(A) is at least an n+1 bit result, then overflow does not occur. That is, an n+1 bit will accommodate 2A, and subtracting sign(A) from 2A never increases the absolute value of 2A. 
     Various examples of calculating 2A-sign(A), in accordance with algorithm 200, where A is less than zero, with the possibility of overflow, are listed below in Table 1. Overflow occurs when the sign bit of A has a different logical value than the sign bit of the result. For illustration purposes, A is a 4-bit operand, and 2A-sign(A) is a 4-bit result. 
     
                       TABLE 1                                                     
______________________________________                                    
CALCULATING2A - SIGN(A) WHERE A IS LESS THAN ZERO                         
WITH POSSIBILITY OF OVERFLOW                                              
______________________________________                                    
Operand   A           A + A                                               
                               ##STR1##                                   
(decimal)                      2A - sign(A)!                              
1000      1000          0111  1110                                        
(decimal -8)                                                              
          ↓    + 0111  ↓                                    
          0111        0 1110  0001                                        
                              (overflow)                                  
1010      1010          0101  1010                                        
(decimal -6)                                                              
          ↓    + 0101  ↓                                    
          0101        0 1010  0101                                        
                              (overflow)                                  
1101      1101          0010  0100                                        
(decimal -3)                                                              
          ↓    + 0010  ↓                                    
          0010        0 0100  1011                                        
                              (decimal -5)                                
1111      1111          0000  0000                                        
(decimal -1)                                                              
          ↓    + 0000  ↓                                    
          0000        0 0000  1111                                        
                              (decimal -1)                                
______________________________________                                    
 
    
     Various examples of calculating 2A-sign(A), in accordance with algorithm 200, where A is less than zero, without the possibility of overflow, are listed below in Table 2. For illustration purposes, A is a 4-bit operand, and 2A-sign(A) is a 5-bit result. 
     
                       TABLE 2                                                     
______________________________________                                    
CALCULATING2A - SIGN(A) WHERE A IS LESS THAN ZERO                         
WITHOUT POSSIBILITY OF OVERFLOW                                           
______________________________________                                    
Operand  A sign   A         A + A                                         
                                   ##STR2##                               
A        extended                                                         
(decimal)                          2A - sign(A)!                          
1000     11000    11000       00111                                       
                                  01110                                   
(decimal -8)      ↓  + 00111                                       
                                  ↓                                
                  00111     0 01110                                       
                                  10001                                   
                                  (decimal -15)                           
1010     11010    11010       00101                                       
                                  01010                                   
(decimal -6)      ↓  + 00101                                       
                                  ↓                                
                  00101     0 01010                                       
                                  10101                                   
                                  (decimal -11)                           
1101     11101    11101       00010                                       
                                  00100                                   
(decimal -3)      ↓  + 00010                                       
                                  ↓                                
                  00010     0 00100                                       
                                  11011                                   
                                  (decimal  -5)                           
1111     11111    11111       00000                                       
                                  00000                                   
(decimal -1)      ↓  + 00010                                       
                                  ↓                                
                  0000      0 00010                                       
                                  11111                                   
                                  (decimal  -1)                           
______________________________________                                    
 
    
     A single example of calculating 2A-sign(A), in accordance with algorithm 200, where A is equal to zero, is listed below in Table 3. For illustration purposes, A is a 4-bit operand, and 2A-sign(A) is a 4-bit result. 
     
                       TABLE 3                                                     
______________________________________                                    
CALCULATING2A - SIGN(A) WHERE A IS EQUAL TO ZERO                          
______________________________________                                    
Operand   A           A + A + 1                                           
                                ##STR3##                                  
(decimal)                       2A - sign(A)!                             
0000      0000          1111   1111                                       
(decimal 0)                                                               
          ↓      1111   ↓                                   
          1111        + 0001   0000                                       
                      1 1111   (decimal 0)                                
______________________________________                                    
 
    
     Various examples of calculating 2A-sign(A) in accordance with algorithm 200, where A is greater than zero, with the possibility of overflow, are listed below in Table 4. Overflow occurs when the sign bit of A has a different logical value than the sign bit of the result. For illustration purposes, A is a 4-bit operand, and 2A-sign(A) is a 4-bit result. 
     
                       TABLE 4                                                     
______________________________________                                    
CALCULATING2A - SIGN(A) WHERE A IS GREATER THAN ZERO                      
WITH POSSIBILITY OF OVERFLOW                                              
______________________________________                                    
Operand   A           A + A + 2                                           
                                ##STR4##                                  
(decimal)                       2A - sign(A)!                             
0111      0111          1000   0010                                       
(decimal 7)                                                               
          ↓      1000   ↓                                   
          1000        + 0010   1101                                       
                      1 0010   (Overflow)                                 
0110      0110          1001   0100                                       
(decimal 6)                                                               
          ↓      1001   ↓                                   
          1001        + 0010   1011                                       
                      1 0100   (Overflow)                                 
0011      0011          1100   1010                                       
(decimal 3)                                                               
          ↓      1100   ↓                                   
          1100        + 0010   0101                                       
                      1 1010   (decimal 5)                                
0001      0001          1110   1110                                       
(decimal 1)                                                               
          ↓      1110   ↓                                   
          1110        + 0010   0001                                       
                      1 1110   (decimal 1)                                
______________________________________                                    
 
    
     Various examples of calculating 2A-sign(A), in accordance with algorithm 200, where A is greater than zero, without the possibility of overflow, are listed below in Table 5. For illustration purposes, A is a 4-bit operand, and 2A-sign(A) is a 5-bit result. 
     
                       TABLE 5                                                     
______________________________________                                    
CALCULATING2A - SIGN(A) WHERE A IS GREATER THAN ZERO                      
WITHOUT POSSIBILITY OF OVERFLOW                                           
______________________________________                                    
Operand A sign   A         A + A + 2                                      
                                   ##STR5##                               
A       extended                                                          
(decimal)                          2A - sign(A)!                          
0111    00111    00111       11000                                        
                                  10010                                   
(decimal 7)      ↓    11000                                        
                                  ↓                                
                 11000     + 00010                                        
                                  01101                                   
                           1 10010                                        
                                  (decimal 13)                            
0110    00110    00110       11001                                        
                                  10100                                   
(decimal 6)      ↓    11001                                        
                                  ↓                                
                 11001     + 00010                                        
                                  01011                                   
                           1 10100                                        
                                  (decimal 11)                            
0011    00011    00011       11100                                        
                                  11010                                   
(decimal 3)      ↓    11100                                        
                                  ↓                                
                 11100     + 00010                                        
                                  00101                                   
                           1 11010                                        
                                  (decimal  5)                            
0001    00001    00001       11110                                        
                                  11110                                   
(decimal 1)      ↓    11110                                        
                                  ↓                                
                 11110     + 00010                                        
                                  00001                                   
                           1 11110                                        
                                  (decimal  1)                            
______________________________________                                    
 
    
     FIG. 3 is a block diagram of a logic circuit 300 for calculating 2A-sign(A) in accordance with an embodiment of the present invention. Inverter circuit 302 includes an operand input coupled to A and generates A at first and second outputs. Data selector circuit 304 includes an input coupled to the sign bit of A, and generates a constant C at its output set to one when A is greater than or equal to zero, and set to zero when A is less than zero. Adder circuit 306 includes first and second operand inputs for receiving A and a third operand input for receiving the constant C. Adder circuit 306 generates A+A+C at a sum output, and A+A+C+1 at a sum-plus-one output. Thus, the sum output provides A+A when A is less than zero, and A+A+1 when A is greater than or equal to zero. Likewise, the sum-plus-one output provides A+A+1 when A is less than zero, and A+A+2 when A is greater than or equal to zero. Multiplexer 308 receives the sum output and sum-plus-one output at first and second operand inputs, and selects one or the other in response to a control input. Inverter circuit 310 includes an operand input coupled to the output of multiplexer 308, and outputs the bit-complement of the output of multiplexer 308. Zero detect circuit 312 determines whether A is zero or nonzero, and control circuit 314 controls multiplexer 308 in response to zero detect circuit 312 and the sign bit of A. Control circuit 314 causes multiplexer 308 to select the sum output when the sign bit of A indicates A is negative or zero detect circuit 312 indicates A is zero, and otherwise causes multiplexer 308 to select the sum-plus-one output when the sign bit of A indicates A is nonnegative and zero detect circuit 312 indicates A is nonzero (thereby indicating A is greater than zero). In this manner, inverter circuit 310 outputs A+A when A is less than zero, A+A+1 when A is equal to zero, and A+A+2 when A is greater than zero. 
     Alternatively, if desired, the sum A+A+C can be provided by arithmetically left-shifting A by one bit position, and applying the left-shifted A (or 2A) and C to first and second operand inputs of adder circuit 306. Also, A+A+1 can be provided by incrementing A+A, and A+A+2 can be provided by incrementing A+A+1. Moreover, zero detect circuit 312 can be modified to inspect carry-out bits from MSB positions of the sum and sum-plus-one outputs of adder circuit 306, instead of inspecting A directly. 
     FIG. 4 is a block diagram of a logic circuit 400 for calculating 2A-sign(A) in accordance with another embodiment of the invention. Logic circuit 400 receives a four-bit operand A, consisting of bits A 3 , A 2 , A 1  and A 0 , and calculates a four-bit result, consisting of bits R 3 , R 2 , R 1  and R 0 . Bits A 3  and R 3  are the MSBs. Logic circuit 400 also generates overflow signal OV. Bit A 3  is applied to inverter 402, bit A 2  is applied to inverter 404, bit A 1  is applied to inverter 406, and bit A 0  is applied to inverter 408. Inverters 402, 404, 406 and 408 generate bits A 3  , A 2  , A 1   and A 0  , respectively. Bit A 3   is applied to first and second operand inputs of half adder 410, bit A 2   is applied to first and second operand inputs of half adder 412, bit A 1   is applied to first and second operand inputs of half adder 414, and bit A 0   is applied to first and second operand inputs of half adder 416. 
     The outputs of half adders 410, 412, 414 and 416 are applied to operand inputs of sum and sum-plus-one adder 418. In particular, sum bit S A  of half adder 410 and carry-out bit C B  of half adder 412 are applied to stage 3 of adder 418, sum bit S B  of half adder 412 and carry-out bit C C  of half adder 414 are applied to stage 2 of adder 418, sum bit S C  of half adder 414 and carry-out bit C D  of half adder 416 are applied to stage 1 of adder 418, and sum bit S D  of half adder 416 is applied to stage 0 of adder 418. Furthermore, bit A 3   is applied to stage 0 of adder 418, thereby providing a constant C of one when A is positive, and providing a constant C of zero when A is negative. Adder 418 generates a sum output, consisting of bits S 3 , S 2 , S 1  and S 0 , and a sum-plus-one output, consisting of bits S+1 3 , S+1 2 , S+1 1  and S+1 0 . Adder 418 also generates first carry-out bit C OUT1  from stage 3 of the sum output, and second carry-out bit C OUT2  from stage 3 of the sum-plus-one output. 
     The sum output and sum-plus-one output are applied to first and second operand inputs of 2:1 multiplexer 420, and select signal SEL is applied to a control input of multiplexer 420. Multiplexer 420 selects the first input thereof and outputs the sum output when signal SEL is a one, and multiplexer 420 selects the second input thereof and outputs the sum-plus-one output when signal SEL is a zero. Multiplexer 420 outputs bits M 3 , M 2 , M 1  and M 0 . Bit M 3  is applied to inverter 422, bit M 2  is applied to inverter 424, bit M 1  is applied to inverter 426, and bit M 0  is applied to inverter 428. Inverters 422, 424, 426 and 428 generate bits R 3 , R 2 , R 1  and R 0 , respectively. 
     OR gate 430 generates signal SEL as a one when bit A 3  is a one, indicating A is negative. OR gate 430 also generates signal SEL as a one when bit A 3  is a zero and EXCLUSIVE-OR gate 432 generates a one, indicating A is zero, when first carry-out bit C OUT1  from A+A+1 and second carry-out bit C OUT2  from A+A+2 have different logical values. Finally, OR gate 430 generates signal SEL as a zero only when bit A 3  is a zero and EXCLUSIVE-OR gate 432 generates a zero, indicating A is greater than zero. 
     Overflow detection is provided by EXCLUSIVE-OR gate 434, which indicates when bits A 3  and R 3  have different logical values. Accordingly, EXCLUSIVE-OR gate 434 generates overflow signal OV at its output. 
     Thus, when A is less than zero, bit A 3  is a one, adder 418 generates A+A at the sum output, signal SEL is a one, multiplexer 420 selects the sum output, inverters 422 to 428 bit-complement A+A, and the result is A+A. When A is equal to zero, bit A 3  is a zero, adder 418 generates A+A+1 at the sum output, signal SEL is a one, multiplexer 420 selects the sum output, inverters 422 to 428 bit-complement A+A+1, and the result is A+A+1. When A is greater than zero, bit A 3  is a zero, adder 418 generates A+A+2 at the sum-plus-one output, signal SEL is a zero, multiplexer 420 selects the sum-plus-one output, inverters 422 to 428 bit-complement A+A+2, and the result is A+A+2. 
     FIG. 5 shows an implementation for adder 418. In this implementation, the sum output is provided by carry lookahead adders that perform fast addition within the basic step time of an instruction cycle. Propagate-generate (PG) sections 502, 504, 506 and 508 receive bits S A  and C B , S B  and C C , S C  and C D , and S D  and A 3  , respectively, and provide propagate and generate signals P 3  and G 3 , P 2  and G 2 , P 1  and G 1 , and P 0  and G 0 , respectively. The propagate and generate signals are furnished to respective stages of first carry chain 510 and second carry chain 512. First carry chain 510 receives a zero as its least significant carry-in bit C IN1 , and generates carry-out bits C 3 , C 2 , C 1  and C 0 . Second carry chain 512 receives a one as its least significant carry-in bit C IN2 , and generates carry-out bits C+1 3 , C+1 2 , C+1 1  and C+1 0 . Carry-out bit C 3  provides first carry-out bit C OUT1 , and carry-out bit C+1 3  provides second carry-out bit C OUT2 . Advantageously, first and second carry-out bits C OUT1  and C OUT2  are generated concurrently. Furthermore, sum generator 514 receives bits S A , C B  and C 2  at stage 3, bits S B , C C , and C 1  at stage 2, bits S C , C D  and C 0  at stage 1, and bits S D  and A 3   and a zero at stage 0. As a result, sum generator 514 generates sum bits S 3 , S 2 , S 1  and S 0 . Likewise, sum generator 516 receives bits S A , C B  and C+1 2  at stage 3, bits S B , C C , and C+1 1  at stage 2, bits S C , C D  and C+1 0  at stage 1, and bits S D  and A 3   and a zero at stage 0. As a result, sum generator 516 generates sum bits S+1 3 , S+1 2 , S+1 1  and S+1 0 . Each stage of sum generators 514 and 516 may include, for instance, first and second two-input EXCLUSIVE-OR gates (not shown), with the inputs of the first EXCLUSIVE-OR gate and the second input of the second EXCLUSIVE-OR gate receiving the bits to be summed, the output of the first EXCLUSIVE-OR gate coupled to the first input of the second EXCLUSIVE-OR gate, and the output of the second EXCLUSIVE-OR gate providing the sum bit. Suitable PG sections, carry chains and sum generators are well-known in the art. 
     The description of the invention set forth herein is illustrative, and is not intended to limit the scope of the invention as set forth in the following claims. A general purpose computer or processor can execute the invention in a single instruction cycle (as is preferred) or multiple instruction cycles. The invention is well-suited for many data processing applications. Variations and modifications of the embodiments disclosed herein may be made based on the description set forth herein, without departing from the scope and spirit of the invention as set forth in the following claims.