Patent Publication Number: US-6665691-B2

Title: Circuit for detecting numbers equal to a power of two on a data bus

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present invention is related to that disclosed in U.S. patent application Ser. No. 09/733,661 entitled “CIRCUIT FOR DETERMINING THE NUMBER OF LOGICAL ONE VALUES ON A DATA BUS” and filed Dec. 8, 2000 . The above application is commonly assigned to the assignee of the present invention. The disclosure of this related patent application is hereby incorporated by reference into the present disclosure as if fully set forth herein. 
    
    
     TECHNICAL FIELD OF THE INVENTION 
     The present invention is directed, in general, to data processors and, more specifically, to a circuit that determines whether or not a number on a data bus is a power of two. 
     BACKGROUND OF THE INVENTION 
     The demand for high performance computers and communication devices requires that state-of-the-art digital signal processors (DSPs) and general purpose microprocessors, such as x86 based microprocessors, execute instructions in the minimum amount of time. A number of different approaches have been taken to decrease instruction execution time, thereby increasing processor throughput. One way to increase processor throughput is to use a pipeline architecture in which the processor is divided into separate processing stages that form the pipeline. Instructions are broken down into elemental steps that are executed in different stages in an assembly line fashion. 
     Pipelining refers to the simultaneous processing of multiple instructions in the pipeline. For example, if a processor executes each instruction in five stages and each stage requires a single clock cycle to perform its function, then five separate instructions can be processed simultaneously in the pipeline, with the processing of one instruction completed during each clock cycle. Hence, the instruction throughput of an N stage pipelined architecture is, in theory, N times greater than the throughput of a non-pipelined architecture that completes only one instruction every N clock cycles. However, the speed improvements provided by pipeline architectures and superpipelining processing are ultimately limited by speed at which the individual stages in the pipeline execute. It is therefore important to minimize the time required to execute each part of an instruction. 
     Mathematical operations often incur substantial time delays in calculating a value. Counting the number of Logic 1 bits on a data bus is a common operation encountered in computer instruction sets (e.g.,  ST 20 C 2  Core Instruction Set Reference Manual , SGS-Thomson Microelectronics, November 1997) and as a component function in various digital blocks, such as memory interface units (e.g., N. J. Richardson,  Private Communication ). The function can serve a number of different purposes, including determining the number of valid bits set in some control logic and performing a simple error detection operation. The input to such a function is an n-bit wide bus in which an arbitrary number of bits are set to a Logic 1 value and the other bits are set to a Logic 0 value. The output for this function is a log 2 (n) bit binary number equal to the number of ones on the input bus. 
     The problem of counting the number of ones on a bus is a simplified analog to the compression tree in a multiplier. Writing the numbers to be added as a vertical row, it is observed that the numbers represent a single column of a multiplier. Designing large multipliers is a well-known problem in digital design (See D. Goldberg,  Appendix A: Computer Arithmetic in Computer Architecture—A Quantitative Approach , by J. L. Hennessy and D. A. Patterson, 2nd Edition, Morgan Kaufmann Publishers Inc., San Francisco, Calif., 1996. See also I. Koren,  Computer Arithmetic Algorithms , Prentice Hall, Englewood Cliffs, N.J., 1993). 
     The procedure for completing the multiplication operation involves two steps. On the first step, the partial products terms are compressed to two terms. This can be done using a number of different compression schemes, including Booth encoding and various trees of full adders, 4:2 carry-save adders (CSA 42 s), 5:3 carry-save adders (CSA 53 s), 7:3 carry-save adders (CSA 73 s), and the like. With two partial products, the final result of the multiplication operation is calculated using a carry-propagate adder (CPA). Again, there is a large literature on the optimum design of adders, including carry-select adders, carry look-ahead adders, and the like. 
     Because the problem of counting the number of Logic 1 bits on a data bus is such a common operation encountered in computer instruction sets, it is important to minimize the execution time of such an operation. However, as the bus grows larger, more stages of adders are required to perform the count and more propagation delays are encountered. 
     A related mathematical operation is the detection of numbers equal to power of 2 on a data bus. In binary notation, a number that is a power of 2 contains one and only one Logic 1 bit. All other bits are Logic 0. Therefore, on an 8-bit bus, a power of 2 would appear as a single Logic 1 bit and seven Logic 0 bits. For example, on an 8-bit bus, 8=2 3 =00001000. Similarly, on an 8-bit bus, 128=2 7 =01000000. A circuit that counts the number of Logic 1 bits on an address bus or data bus can also be used to detect powers of two on the bus. Powers of two represent the special case where the count of Logic 1 bits on the bus equals one. 
     Therefore, there is a need in the art for data processors that minimize the execution time of common mathematical operations. In particular, there is a need for a circuit capable of rapidly determining the number of Logic 1 bits on a bus in a microprocessor, memory interface, or other data processing device. More particularly, there is a need for a Logic 1 bit counting circuit that minimizes the number of stages required to count Logic 1 bits on a data bus. Moreover, there is a need for a circuit capable of rapidly determining that there is one and only one Logic 1 bit on a bus in a microprocessor, memory interface, or other data processing device in order to detect values that are equal to a power of two. 
     SUMMARY OF THE INVENTION 
     The present disclosure uses the following abbreviations and definitions to designate adder cells: 
     1. HA—Half adder. A half adder adds two input bits and provides the result as a two bit output, generally called sum (S) and carry (C). Carry has a weight of 2 and sum has a weight of 1. 
     2. CSA 32 —Full adder. A full adder that counts three input bits and provides the result (i.e., the number of Logic 1 bit) as a two bit output. The outputs are generally called the sum and carry, with the carry having a weight of 2 and the sum of 1. 
     3. CSA 42 —4:2 carry-save adder. A 4:2 carry-save adder is a 4-to-2 (4:2) compressor circuit that adds the result of five input bits (four regular bits and a carry-in (CIN) bit) and produces three output bits (a carry bit and a sum bit, and a carry-out (COUT) bit) for the result. The COUT bit has a weight of 2, the carry bit has a weight of 2, and the sum bit has a weight of 1. 
     4. CSA 53 —5:3 carry-save adder. A 5:3 carry-save adder is a 5-to-3 compressor circuit that adds five input bits, three of which have bit weights of 1 and two of which have bit weights of 2. The three output bits have bit weights of 4, 2 and 1. 
     5. CSA 73 —7:3 carry-save adder. A 7:3 carry-save adder is a 7-to-3 compressor circuit that counts seven input bits, each having a bit weight of 1. The three outputs bits have bit weights of 4, 2, and 1. 
     6. CPA—Carry-propagate adder. An adder circuit that gives the binary result of adding two binary numbers. 
     7. CSA 43 —4:3 carry-save adder. A 4:3 carry-save adder is a 4-to-3 compressor circuit that adds four input bits and provides three outputs (S 2 , S 1 , and S 0 ) having bit weights of 4, 2 and 1, respectively. This compressor is not efficient for general purpose multiplication, but is one of a family of compressors, introduced in the present application (along with the CSA 63  and CSA 84 ), shown to have advantages when used to count the number of Logic 1 bits on a bus. 
     8. CSA 63 —6:3 carry-save adder. A 6:3 carry-save adder is a 6-to-3 compressor circuit that adds six equally weighted input bits and produces three output bits with weights of 4, 2, and, 1, respectively. 
     9. CSA 84 —8:4 carry-save adder. An 8:4 carry-save adder is an 8-to-4 compressor circuit with adds eight equally weighted input bits. The output bits have weights of 8, 4, 2 and 1, respectively. 
     To address the above-discussed deficiencies of the prior art, it is a primary object of the present invention to provide a circuit for determining if an N-bit number is equal to a power of two. According to an advantageous embodiment of the present invention, the circuit comprises: 1) a first stage of detection gates, each of the first stage detection gates capable of receiving a first data bit and a second data bit from the N-bit number and generating a first output bit and a second output bit, wherein the first and second output bits are 01 if the first and second data bits are different and are one of 00 and 11 if the first and second data bits are the same; and 2) a second stage of detection gates coupled to the outputs of the first stage of detection gates, each of the second stage detection gates receiving three of the first stage output bits and generating a first output bit and a second output bit, wherein the first and second output bits of the second stage detection gates are 01 if only one of the three first stage output bits is equal to Logic 1 and are one of 00 and 11 otherwise. 
     According to one embodiment of the present invention, each of the detection gates in the first stage of detection gates comprises a first multiplexer and a second multiplexer. 
     According to another embodiment of the present invention, the first multiplexer has a 0 input channel coupled to the first data bit, a 1 input channel coupled to a Logic 1 signal, and a channel select input coupled to the second data bit. 
     According to still another embodiment of the present invention, the second multiplexer has a 0 input channel coupled to a Logic 0 signal, a 1 input channel coupled to the first data bit, and a channel select input coupled to the second data bit. 
     According to yet another embodiment of the present invention, each of the detection gates in the second stage of detection gates comprises a first multiplexer and a second multiplexer. 
     According to a further embodiment of the present invention, the first multiplexer has a 0 input channel coupled to a first output bit of the first stage, a 1 input channel coupled to a Logic 1 signal, and a channel select input coupled to a second output bit of the first stage. 
     According to a still further embodiment of the present invention, the second multiplexer has a 0 input channel coupled to a third output bit of the first stage, a 1 input channel coupled to the first output bit of the first stage, and a channel select input coupled to the second output bit of the first stage. 
     According to a yet further embodiment of the present invention, each of the detection gates in the second stage of detection gates further comprises a third multiplexer and a fourth multiplexer. 
     In another embodiment of the present invention, the third multiplexer has a 0 input channel coupled to an output of the first multiplexer, a 1 input channel coupled to a Logic 1 signal, and a channel select input coupled to a fourth output bit of the first stage. 
     In still another embodiment of the present invention, the fourth multiplexer has a 0 input channel coupled to an output of the second multiplexer, a 1 input channel coupled to the output of the first multiplexer, and a channel select input coupled to the fourth output bit of the first stage. 
     The foregoing has outlined rather broadly the features and technical advantages of the present invention so that those skilled in the art may better understand the detailed description of the invention that follows. Additional features and advantages of the invention will be described hereinafter that form the subject of the claims of the invention. Those skilled in the art should appreciate that they may readily use the conception and the specific embodiment disclosed as a basis for modifying or designing other structures for carrying out the same purposes of the present invention. Those skilled in the art should also realize that such equivalent constructions do not depart from the spirit and scope of the invention in its broadest form. 
     Before undertaking the DETAILED DESCRIPTION OF THE INVENTION below, it may be advantageous to set forth definitions of certain words and phrases used throughout this patent document: the terms “include” and “comprise,” as well as derivatives thereof, mean inclusion without limitation; the term “or,” is inclusive, meaning and/or; the phrases “associated with” and “associated therewith,” as well as derivatives thereof, may mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, or the like; and the term “controller” means any device, system or part thereof that controls at least one operation, such a device may be implemented in hardware, firmware or software, or some combination of at least two of the same. It should be noted that the functionality associated with any particular controller may be centralized or distributed, whether locally or remotely. Definitions for certain words and phrases are provided throughout this patent document, those of ordinary skill in the art should understand that in many, if not most instances, such definitions apply to prior, as well as future uses of such defined words and phrases. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     For a more complete understanding of the present invention, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, wherein like numbers designate like objects, and in which: 
     FIG. 1 illustrates an exemplary processing system, namely a personal computer, that implements an improved Logic 1 counter in accordance with the principles of the present invention; 
     FIG. 2 illustrates in greater detail an exemplary processor according to one embodiment of the present invention; 
     FIG. 3 illustrates a Logic 1 counter for counting Logic 1 bits on a 16-bit bus according to one embodiment of the prior art; 
     FIG. 4 illustrates a Logic 1 counter for counting Logic 1 bits on a 16-bit bus and detecting values that are equal to a power of two according to one embodiment of the present invention; and 
     FIG. 5 illustrates a circuit for detecting a power of two value on an 8-bit bus according to an alternate embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIGS. 1 through 5, discussed below, and the various embodiments used to describe the principles of the present invention in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the invention. Those skilled in the art will understand that the principles of the present invention may be implemented in any suitably arranged data processor. 
     FIG. 1 illustrates an exemplary processing system, namely personal computer (PC)  100 , that contains an improved Logic 1 counter in accordance with the principles of the present invention. Personal computer  100  comprises removable (i.e., floppy) disk drive (FDD)  102  and hard disk drive (HDD)  103 , monitor  104 , keyboard  105 , processor (CPU)  106 , main memory  107 , and a pointing device, such as mouse  108 . Monitor  104 , keyboard  105 , and mouse  108  may be replaced by, or combined with, other input/output (I/O) devices. Removable disk drive  102  is capable of reading and writing to removable floppy diskettes. Hard disk drive  105  provides fast access for storage and retrieval of application programs and data. 
     Keyboard  105  and mouse  108  are coupled to PC  100  via input/output (I/O) interface (IF)  110 . Monitor  104  is coupled to pc  100  via video/audio interface (IF)  112 . The internal components of PC  100 , including floppy disk drive  102 , hard disk drive  103 , processor  106 , main memory  107 , I/O interface  110  and video/audio interface  112 , are coupled to and communicate across communications bus  115 . 
     In an exemplary embodiment of the present invention, main memory  107  comprises a volatile storage device, such as a dynamic random access memory (RAM). Processor  106  may comprise an on-board two level cache system, including a Level  1  (L 1 ) cache and a Level  2  (L 2 ) cache. The two level cache is a system in which a small, fast cache (the L 1  cache) is connected to a slower, larger cache (the L 2  cache). When the central processing unit (CPU) core logic of processor  106  reads or writes data to or from a memory location in main memory  107 , the cache system first tests to see if the data belonging to that location is in the L 1  cache. If the data is in the L 1  cache, then the data is provided or updated quickly by the L 1  cache. If the data is not in the L 1  cache, then an L 1  cache read “miss” or an L 1  cache write “miss” has occurred. 
     The data is then provided or updated to the CPU core logic of processor  106  by the L 2  cache. In the case of an L 1  cache read miss, the line containing the requested data is also transferred from the L 2  cache to the L 1  cache, so that the data may be provided more quickly the next time processor  106  accesses the data. This is known as an L 1  cache line fill. If the data is also not in the L 2  cache, then an L 2  cache miss has occurred and the line containing the requested data is fetched from main memory  107  and then loaded into the L 2  cache for faster access the next time the data is requested. This is known as an L 2  cache line fill. 
     FIG. 2 illustrates in greater detail exemplary processor  106  according to one embodiment of the present invention. Processor  106  contains an instruction pipeline comprising instruction fetch (IF) stage  205 , decode stage  210 , operand fetch stage  215 , execute stage  220 , and write-back stage  225 . Processor  106  also comprises register stack  230 , instruction (INSTR.) cache  235  and data cache  240 . 
     Processor  106  is a central processing unit (CPU) capable of fetching and interpreting instructions, retrieving data, executing instructions, and storing results. The illustrated instruction pipeline is a mechanism capable of executing several different operations concurrently. The pipeline does this by breaking down the processing steps for each major task into several discrete processing phases, each of which is executed by a separate pipeline stage. Each task must pass sequentially through each processing phase, and hence each pipeline stage, to complete its execution. 
     Instruction fetch stage  205  fetches instructions to be executed from instruction cache  235  and stores the fetched instructions in an instruction fetch buffer (IFB). The instructions taken from the IFB by decode stage  210  are encoded in a highly compact form. Decode stage  210  decodes the instructions into larger sets of signals that can be used directly for execution by subsequent pipeline stages. Operand fetch stage  215  fetches operands from memory or from register stack  230 . Execute stage  220  performs the actual operation (e.g., add, multiply, divide, and the like) on the operands fetched by operand fetch stage  215  and generates the result. Write-back stage  225  writes the result generated by execute stage  220  into data cache  240  or into one of the registers in register stack  230 . 
     As noted above, it is important to minimize the time required to execute each part of an instruction. In exemplary processor  106 , there are a number of data buses and address buses interconnecting the functional blocks within processor  106 . Many programs contain instructions that count the number of Logic 1 bits on a data bus, either for status purposes, or error checking purposes, or the like. Furthermore, some program instructions are used to detect if a number is a power of two. This can be accomplished by counting the number of Logic 1 bits on a bus and determining if the count is equal to 1. If so, then the number on the bus is a power of 2. However, as noted above, counting the number of Logic 1 bits on a data bus is a mathematical operation that may cause undue delay if the circuit that counts the Logic 1 bits is not efficiently constructed in order to minimize the number of gate delays (i.e., stages). 
     The present invention determines the number of Logic 1 bits on a bus (address or data) using a novel set of compressors. The present invention significantly simplifies the process of compressing the partial product terms. The resulting solution is faster, and also generally smaller and more power efficient solution than conventional solutions to the problem of determining the number of Logic 1 bits on an address or data bus. 
     According to the principles of the present invention, the encoding scheme involves dividing the input bus into M segments each of which are N-bits wide. A first stage of logic circuits is used to count the number of Logic 1 bits in each of these N-bit segments. Usually, N is chosen as a multiple of 4 (e.g., 8, 16, 24, 32, and the like). While this is similar to how a traditional multiplier compressor works, the fact that the first stage of compressors work on data bits that are only a single bit wide (i.e., bit weight of 1) permits the subsequent use of compressors that generally are not favored in multipliers. 
     This is due to the fact that the first stage of compressors do not need to consider the compression ratio being proportional to the number of output bits. In regular multiplication, when, for example, a 4:2 carry-save adder (CSA 42 ) gate is used in a stage, the output data is 2 bits wide. This ensures that the compression that occurs is 4 to 2 (i.e., 2-to-1 ratio). In a CSA 42 , there is also a carry-in (CIN) bit and carry-out (COUT) bit which are used by other gates in the same stage. Since these bits are internally generated in the row and are not available as inputs or outputs, they are not included in the compression ratio calculation. 
     This problem does not occur when adding data one bit wide, as there are no other rows of data which need to be tiled. Standard multiplier compressors are designed to accommodate the wide data widths present in a multiplication operation. In a one bit counter, the first compression that occurs is always down to a single bus. Thus, a CSA 42  compressor actually performs compression of 4-to-1 for the first compression. After the first compression is completed, the partial products are now of width greater than one. Under these conditions, the usual compression schemes for multipliers needs to be utilized. 
     Another advantage of having data being one bit wide is that there are no carry-in bits. This permits the reduction of the amount of computation relative to compressors with carry-in bits. Since the first compression allows for maximum compression, there are some advantages to be garnered by making the first compressor as wide as possible. For example, a four input CSA 43  may be used. For traditional multipliers, a compressor that receives 4 bits, but which gives a meager compression ration of {fraction (4/3)}=1.33, is a worse compressor than a common full adder (CSA 32 ), and would never be used. 
     In general, it is advantageous to use large compressors up front. For example, a CSA 84  which gives the four bit result of adding the eight inputs can be used to perform an initial 8 to 1 compression. For standard partial product compression, a CSA 84  has no advantage over a CSA 42  in terms of compression ration, and due to the extra circuit complexity would not be used. However, in the present invention, a CSA 84  serves a very advantageous task. Other useful compressor sizes for the initial compression would be a CSA 63 , which takes six inputs and compresses them to three outputs. 
     The present invention uses novel compressors for the first stage of the compression tree and then uses standard compression circuits in subsequent stages. To demonstrate the advantages of the present invention, a prior art counter for counting Logic 1 bits on a 16-bit bus is compared to a 16-bit bus counter according to the principles of the present invention. In the prior art counter, a first stage of CSA 42  adders is used. The actual optimal implementation for a particular technology may or may not use CSA 42  gates, since it is dependent on the width of the data bus and the delay characteristics of the technology. The example is, however, used to demonstrate the general superiority of the present invention, irrespective of the actual compression scheme used for the partial products of width greater than 1. 
     FIG. 3 illustrates Logic 1 counter  300  for counting Logic 1 bits on a 16-bit bus according to one embodiment of the prior art. Logic 1 counter  300  comprises four stages of adders. A first stage comprises four 4:2 carry-save adders, namely CSA 42   301 , CSA 42   302 , CSA 42   303  and CSA 42   304 . A second stage comprises two 4:2 carry-save adders, namely CSA 42   305  and CSA 42   306 , and two half adders, namely HA  311  and HA  312 . A third stage comprises two 4:2 carry-save adders, namely CSA 42   307  and CSA 42   308 , and a half adder, namely HA  313 . The fourth stage is 4-bit carry-propagate adder (CPA)  321 , which receives a 3-bit argument on a first 4-bit input and a second 4-bit argument on a second 4-bit input. The sum of the two arguments is a five bit result at the output of 4-bit adder  321 . 
     In the prior art circuit, a tree of CSA 42  cells is used to compress the 16 bits received from a bus to a sum and carry term. In the first stage, four CSA 42  cells operate in parallel and reduce the number of partial products to eight. The reason there are eight partial product terms is that each CSA 42  cell produces a carry bit and a carry-out bit, both of which have weights of 2. Since we have four CSA 42  cells, we have eight terms of the same weight. The second stage uses two CSA 42  cells and two HA cells in parallel to reduce to four partial products. 
     The third stage uses two CSA 42  cells and one HA cell to produce two 4-bit outputs. The final addition uses a 4-bit CPA with a carry-out bit. In some process technologies, the delay of a CSA 42  cell may be 0.72 nanoseconds and the delay of a CPA adder may be 0.77 nanoseconds. Since the critical path in Logic 1 counter  300  is three CSA 42  cells followed by a 4-bit CPA, the total delay is 2.93 nanoseconds (0.72+0.72+0.72+0.77). 
     FIG. 4 illustrates Logic 1 counter  400  for counting Logic 1 bits on a 16-bit bus and detecting numbers equal to a power of two according to one embodiment of the present invention. Logic 1 counter  400  comprises three stages of adders. A first stage comprises four 4:3 carry-save adders, namely CSA 43   401 , CSA 43   402 , CSA 43   403  and CSA 43   404 . A second stage comprises three 4:2 carry-save adders, namely CSA 42   411 , CSA 42   412 , and CSA 42   413 . The third stage is 4-bit carry-propagate adder (CPA)  421 , which receives a 3-bit argument on a first 4-bit input and a second 4-bit argument on a second 4-bit input. The sum of the two arguments is a five bit result at the output of 4-bit CPA 42 1. 
     By using four CSA 43  cells for the first stage, it is possible to reduce the 16 partial products to four. In the second stage, three CSA 42  cells operate in parallel to reduce the result to two partial products. A 4-bit CPA cell generates the final result. A synthesized CSA 43  cell may have a delay of 0.48 nanoseconds in a typical fabrication process. Logic 1 counter  400  has a critical path of one CSA 43  cell, one CSA 42  cell, and one 4-bit CPA. This equals a total delay of 1.97 nanoseconds (0.48+0.72+0.77), which is faster that the prior art counter. The design uses four CSA 43  cells and three CSA 42  cells compared to eight CSA 42  cells and 2 HA adders in the prior art design. Since the CSA 43  cell has approximately the same complexity as a CSA 42  cell, the new design is also smaller and consumes less power. 
     Alternately, Logic 1 counter  400  could have been implemented with full adders (or CSA 32  cells) and half adders. For a prior art implementation with those cells, the first stage would use four CSA 32  cells and one HA cells in parallel. The second stage would use two CSA 32  cells and 2 HA cells. The third stage of compression would use one CSA 32  cell and 2 HA cells. The fourth and final stage would need one CSA 32  cell and one HA cell. Finally a 4-bit CPA would be needed to complete the function. The critical path would thus be four CSA 32  cells and a 4-bit carry-propagate adder. A typical CSA 32  cell has a delay of 0.32 nS. Thus, the full delay is 2.05 nanoseconds. 
     On the other hand, using CSA 43  cells in the first stage according to the principles of the present invention, the first stage compression could be performed with four CSA 43  cells. The second stage would use four CSA 32  cells. The third stage would need two CSA 32  cells and a HA cell before passing the result on to the 4-bit CPA. The critical path in this case is one CSA 43  cell, two CSA 32  cells, and the CPA, which give a delay of 1.89 nanoseconds. Again, the use of the new first stage compressor results in a faster implementation. In terms of cell count, the pure CSA 32  solution requires eight CSA 32  cells, six HA cells, and a 4-bit CPA. The solution according to the present invention using CSA 43  cells needs four CSA 43  cells, six CSA 32  cells, one HA cell and a 4-bit CPA. 
     The two examples in the previous subsection show speedups of 36% and 8% in using the CSA 43  compressor for counting the number of Logic 1 bits on a bus. The actual speed improvements vary depending on the bus width, the fabrication technology, and the compression scheme being used. 
     In addition to the CSA 43  cell described herein, the CSA 63  cell and the CSA 84  cell are also useful in the first compression stage. In general, one can extend the result to a CSApq cell, where p input bits are compressed to q output bits. The basic result of the present invention is that for the first compression stage of an application where the partial products have a width of one, the actual compression achieved is p/1 and not p/q. Thus, a whole host of p values and q values can be used which would not necessarily be of any advantage in regular multiplication where the partial product widths are always greater than 1. 
     Logic 1 counter  400  can also be used to detect numbers equal to a power of 2. This can be done by comparing the result counted by Logic 1 counter  400  with the value 1. If the count of Logic 1 bits on a data bus is equal to 1, then that number on the data bus is a power of 2. However, Logic 1 counter  400  is not the only type of circuit that may be used to determine that one and only one bit on a data bus is equal to Logic 1 (i.e., number on data bus is a power of 2). Other circuits are capable of determining that one and only one bit on a data bus is equal to Logic 1. 
     FIG. 5 illustrates circuit  500  for detecting a power of two value on an 8-bit bus according to an alternate embodiment of the present invention. Circuit  500  comprises a plurality of multiplexers arranged in three stages. The first stage comprises multiplexers (MUXs)  501 - 508 . The second stage comprises multiplexers (MUXs)  521 - 524  and multiplexers (MUXs)  531 - 534 . The third stage comprises multiplexers (MUXs)  541 - 544 . 
     The first stage of eight multiplexers (MUX  501  through MUX  508 ) receives data bits D 0  to D 7  from the 8-bit bus. MUX  501  through MUX  508  are organized as four pairs of multiplexers. Each pair of multiplexers receives two data bits and produces a 2-bit result that indicates one or three states: that the two received data bits contain no Logic 1 bits, that the two received data bits contain only one Logic 1 bit, or that the two received data bits contain two Logic 1 bits. 
     The present invention may be better understood by describing the operation of MUX  507  and MUX  508 . The D 1  bit is used as a MUX select signal on MUX  507  and MUX  508 . When D 1 =0, the 0 channel is selected on MUX  507  and MUX  508 . When D 1 =1, the 1 channel is selected on MUX  507  and MUX  508 . The 0 channel of MUX  507  is connected to Logic 0 (i.e., tied low). The 1 channel of MUX  507  is connected to the D 0  bit. The 0 channel of MUX  508  is connected to the D 0  bit. The 1 channel of MUX  508  is connected to Logic 1 (i.e., tied high). The output of MUX  507  is the result  1 . The output of MUX  508  is the result P 0 . TABLE 1 below is a truth table defining the operation of MUX  507  and MUX  508 : 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 D1 
                 D0 
                 P1 
                 P0 
               
               
                   
                   
               
             
            
               
                   
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 0 
                 1 
                 0 
                 1 
               
               
                   
                 1 
                 0 
                 0 
                 1 
               
               
                   
                 1 
                 1 
                 1 
                 1 
               
               
                   
                   
               
            
           
         
       
     
     If (D 1 ,D 0 )=00 (i.e., both Logic 0), then (P 1 ,P 0 )=00. If (D 1 ,D 0 )=11 (i.e., both Logic 1), then (P 1 ,P 0 )=11. If one and only one of D 1  and D 0  are equal to Logic 1 (i.e., 01 or 10), then (P 1 ,P 0 )=01. Thus, the outputs of MUX  507  and MUX  508 , namely P 1  and P 0 , have only three states: 00, 01 and 11. The state (P 1 ,P 0 )=10 does not occur. 
     The operations of the other three pairs of multiplexers (i.e., MUX  501  and MUX  502 , MUX  503  and MUX  504 , and MUX  506  and MUX  507 ) in the first stage are identical to the operation of MUX  507  and MUX  508 . This being the case, each of the output pairs of the other three multiplexer pairs also has only three states, namely 00, 01 and 11. The state (P 7 , P 6 )=10 does not occur, the state (P 5 , P 4 )=10 does not occur, and the state (P 3 , P 2 )=10 does not occur. 
     The second stage of multiplexers, MUX  521 - 524  and MUX  531 - 534 , receives the result bits P 0  through P 7  from the first stage of multiplexers. MUX  521 - 524  operate on P 7 -P 4  to produce two result bits, Q 3  and Q 2 . MUX  531 - 534  operate on P 3 -P 0  to produce two result bits, Q 1  and Q 0 . 
     The operation of the second stage may be better understood by describing the operation of MUX  531 -MUX  534 . The P 3  bit is used as a MUX select signal on MUX  533  and MUX  534 . The P 2  bit is used as a MUX select signal on MUX  531  and MUX  532 . The 1 channel of MUX  532  is connected to Logic 1 (i.e., tied high). The 0 channel of MUX  532  is connected to the P 0  bit. The 0 channel of MUX  531  is connected to the P 1  bit. The 1 channel of MUX  531  is connected to the P 0  bit. The output of MUX  531  is applied to the 0 channel of MUX  533 . The output of MUX  532  is applied to the 1 channel of MUX  533  and the 0 channel of MUX  534 . The 1 channel of MUX  534  is set to Logic 1. 
     The output of MUX  533  is the result Q 1 . The output of MUX  534  is the result Q 0 . TABLE 2 below is a truth table defining the operation of MUX  531 -MUX  534 . Dashed entries indicate (1,0) states in a standard Boolean truth table that are disallowed because neither (P 3 , P 2 ) nor (P 1 ,P 0 ) can ever be equal to 10: 
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 P3 
                 P2 
                 P1 
                 P0 
                 Q1 
                 Q0 
               
               
                   
                   
               
             
            
               
                   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
               
               
                   
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
               
               
                   
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                   
               
            
           
         
       
     
     If (P 3 , P 2 , P 1 , P 0 )=0000, then (Q 1 , Q 0 )=00. If two or more of P 3 , P 2 , P 1  and P 0 =1, then (Q 1 , Q 0 )=11. If one and only one of P 3 , P 2 , P 1  and P 0 =1, then (Q 1 , Q 0 )=01. Thus, the outputs of MUX  533  and MUX  534 , namely Q 1  and Q 0 , have only three states: 00, 01 and 11. The state (Q 1 , Q 0 )=10 does not occur. 
     The operations of MUX  521 , MUX  522 , MUX  523  and MUX  524  are identical to the operations of MUX  531 , MUX  532 , MUX  533  and MUX  534 . This being the case, Q 3  and Q 2  also have only three states, namely 00, 01 and 11. The state (Q 3 , Q 2 )=10 does not occur. 
     The third stage of multiplexers, MUX  541 -MUX  544 , receives the result bits Q 0 , Q 1 , Q 2 , and Q 3  from the second stage of multiplexers. MUX  541 -MUX  544  operate on Q 3 -Q 0  to produce two result bits, R 1  and R 0 . The operations of MUX  541 , MUX  542  , MUX  543  and MUX  544  are identical to the operations of MUX  531 , MUX  532 , MUX  533  and MUX  534  in the second stage. TABLE 3 below is a truth table defining the operation of MUX  541 -MUX  544 . Dashed entries indicate (1, 0) states in a standard Boolean truth table that are disallowed because neither (Q 3 , Q 2 ) nor (Q 1 , Q 0 ) can ever be equal to 10: 
     
       
         
           
               
               
               
               
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 Q3 
                 Q2 
                 Q1 
                 Q0 
                 R1 
                 R0 
               
               
                   
                   
               
             
            
               
                   
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                   
                 0 
                 0 
                 0 
                 1 
                 0 
                 1 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
               
               
                   
                 0 
                 1 
                 0 
                 1 
                 1 
                 1 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 1 
                 1 
                 0 
                 0 
                 1 
                 1 
               
               
                   
                 1 
                 1 
                 0 
                 1 
                 1 
                 1 
               
               
                   
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
                   
               
            
           
         
       
     
     In sum, if (R 1 , R 0 )=01, then there is exactly one Logic 1 bit in data bits D 0  to D 7  on the 8-bit bus, which means the number on the 8-bit bus is a power of two. If (R 1 , R 0 )=11, then there is more than one Logic 1 bit in data bits D 0  to D 7  and the number on the 8-bit bus is not a power of two. If (R 1 , R 0 )=00, then there are no Logic 1 bits in data bits D 0  to D 7  and the number on the 8-bit bus is zero. As before, the state (R 1 , R 0 )=10 cannot occur. The (R 1 , R 0 ) result bits can be reduced to a single flag bit indicating that the number on D 7 :D 0  is a power of two by applying R 1  and R 0  to an exclusive-OR gate. 
     It is important to note that the input data bits, D 0  through D 7 , do not need to be applied to the input multiplexers in sequential order. That is, adjacent data bits, such as D 2  and D 2  or D 6  and D 7 , do not have to be processed by the same one of MUX  501 -MUX  508 . Even if data bits D 0  through D 7  are applied randomly to MUX  501 -MUX  508 , the present invention still operates to determine if D 7 :D 0  is a power of two. 
     Although the present invention has been described in detail, those skilled in the art should understand that they can make various changes, substitutions and alterations herein without departing from the spirit and scope of the invention in its broadest form.