Abstract:
The invention relates to an adder for adding at least four bits of the same significance w, said adder having a first number of inputs for receiving the bits of the same significance w that are to be added and a number of outputs, the bits to be added being applied to the inputs in presorted form, and the adder adding the bits while taking account of the presorting. The invention also provides an adding device for adding at least four bits of equal significance and a corresponding method.

Description:
The invention relates to a device and a method for adding a plurality of bits of equal significance. The invention relates, in particular, to an adder having a small number of controllable paths between an output and a supply voltage. 
   BACKGROUND 
   Adders are known in the art and are generally used to add a particular number of bits of equal significance, with the sum value (in the form of a sum bit) and a particular number of requisite carry bits being output. By way of example, “three-to-two bit full adders” are known, said adders having three inputs for receiving three bits of equal significance w and two outputs for outputting a sum bit of significance w and a carry bit of significance 2w. In this case, the sum bit of significance w indicates the parity of the sum of the three input bits of significance w, and the carry bit indicates the carry of significance 2w. Further carry outputs are required if more than three bits of equal significance are to be added. In order to make the most efficient use possible of the representational space for the carry bits, it is appropriate to output a sum bit and two carry bits of significance 2w and 4w when adding seven bits of equal significance. 
   EP 0514061 describes a “seven-to-three bit adder”. In this case, the input bits of equal significance that are to be added are routed to the outputs through six logic gate stages. 
   The present invention is now based on the object of providing a simple multibit adder. In particular, the adder is to require little implementation complexity and is to have particularly short signal propagation times and a low power consumption. 
   SUMMARY 
   According to the invention, this object is achieved by means of an adder, an adding device and a corresponding method. 
   Accordingly, an adder for adding at least four bits of equal significance is provided, said adder having a first number of inputs for receiving the bits of significance w that are to be added and having a second number of outputs, the bits to be added being applied to the inputs in presorted form, and the adder adding the bits to be added while taking account of the presorting. 
   An adding device for adding at least four bits of the same significance is furthermore provided, said adding device having at least one first adder and one first sorter, with the sorter being connected upstream of the adder and presorting the bits to be added. 
   A method for adding at least four bits of equal significance is also provided, said method having the following method steps:
     (a) providing at least four bits of significance w that are to be added,   (b) presorting the bits to be added,   (c) calculating the sum and carry using the presorting,   (d) outputting a sum bit, and   (e) outputting at least two carry bits.   

   Efficiently presorting the bits to be added in the inventive adder or method and calculating the sum and carries using the presorting make it possible to greatly reduce the circuit complexity in comparison with adders based on the prior art. This is highly advantageous, in particular, when a plurality of inventive adders are connected in series. 
   Since, in comparison with seven-bit adders based on the prior art, for example, fewer controllable paths are required, an inventive adder has a particularly high switching speed and a low power consumption. 
   In one preferred embodiment of the inventive adder, the number of inputs corresponds to the number of bits to be added, and the number of outputs has been selected in such a manner that the addition&#39;s parity and carry can be represented in full. In particular, the inventive adder advantageously has at least six inputs and at least three outputs for six bits to be added. 
   In another preferred embodiment of the inventive adder, a sum bit of significance w is applied to a first output, and carry bits of significance 2w and 4w are applied to a second and a third output. Selecting the significances 2w and 4w at the second and third outputs makes full use of the representational space for the addition&#39;s carry. 
   In yet another preferred embodiment of the inventive adder, one output is provided for outputting a sum bit of significance w, and second, third and fourth outputs are provided for outputting carry bits of significance 2w. 
   Outputting the carry in the form of three carry bits of equal significance 2w advantageously makes it possible to sort the carry bits in a particularly efficient manner. This makes it possible to route the carry to further adders according to the invention and thus to carry out a further addition using the presorting. 
   In a preferred presorting operation, the bits to be added have always been presorted in such a manner that the same logic levels are applied at least to two adjacent inputs of three adjacent inputs of the adder. This preferred presorting operation also makes it possible to advantageously supply the adder with the three carry bits from an inventive addition of less significance, said bits being present in such sorted form. 
   In one particularly preferred embodiment of the adder, the adder has three first inputs, three second inputs and a third input. The bits to be added are always present at the three first and three second inputs in presorted form in such a manner that the same logic levels are applied at least to two adjacent inputs of the first three and the second three inputs. A seventh bit to be added is then applied to the third input. 
   This particularly preferred embodiment of the inventive adder makes it possible for the circuit complexity to be achieved to a maximum of five controlled paths of controllable switches in series between one of the outputs and a supply connection. These controlled paths form only two logic gates. As a result, the signal propagation time is considerably shorter than in seven-bit adders based on the prior art, which have at least six logic gates between an output and a supply connection. In addition, this preferred embodiment of the inventive adder is distinguished by its low power consumption. It is furthermore advantageous that the adder may be in the form of a carry-save adder. 
   One preferred development of the invention provides an adding device for adding at least four bits of the same significance w, said adding device having at least one first inventive adder and one first sorter which is connected upstream of the adder and presorts the bits to be added. 
   This has the advantage that even bits to be added that have not been presorted at the input can be added quickly and without a great deal of circuit complexity, in accordance with the invention, by the inventive adding device. 
   One particularly preferred development of the adding device provides two sorters which each have three inputs and three outputs and are connected upstream of six inputs of the adder. In this case, the sorters presort the bits to be added. Three carry bits of the same significance 2w can thus advantageously be routed to one of the two sorters. This makes it possible for the inventive adding device also to be used in combination with conventional adders which provide carry bits. 
   Another preferred development of the adding device provides further adders for adding bits of the significance of multiples of 2w, said further adders being connected in cascade to one another. In this case, the three carry outputs—of significance 2w—of the first adder are coupled to inputs of the second adder which performs adding of significance 2w. The adders are advantageously part of an integrated circuit. The cascaded embodiment of the inventive adding device makes particularly efficient use of the advantageous short switching time and low power consumption of the adders. 
   In one advantageous refinement of the inventive method for adding at least six bits of equal significance, the bits to be added are presorted in such a manner that three first bits are combined to form a first group, three further bits are combined to form a second group, and the eight combinations—or states—of bits from each group which result in the same sum are assigned to four subgroups. 
   The three bits in each group may have eight different combinations. Each combination is assigned to a subgroup, with each combination in the same subgroup giving the same addition result. That is to say only four subgroups are relevant to the inventive addition. The addition is therefore simplified in the case of such an advantageous presorting operation. Moreover, an addition table which has been reduced from 2 7 =128 “conventional states” to 32 “inventive states” may be specified on the basis of the subgroups. 
   The subclaims specify further advantageous refinement of the invention. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention is described below using exemplary embodiments and with reference to the drawings, in which: 
       FIG. 1 : shows a sorting table for an inventive sorter, 
       FIG. 2 : shows an inventive addition table, 
       FIG. 3 : shows a block diagram of the inventive adding device, 
       FIG. 4 : shows a block diagram of an inventive sorter, 
       FIGS. 5   a - c:  show a preferred embodiment of the sorting circuit, 
       FIG. 6 : shows a block diagram of the inventive adder, and 
       FIGS. 7   a - d:  show a preferred embodiment of the adder&#39;s summing circuit and carry bit circuits. 
   

   DETAILED DESCRIPTION 
     FIG. 1  describes the sorting of three bits AQ′, BQ′, CQ′ of equal significance. The three bits AQ′, BQ′, CQ′ may be present in eight combinations or states Z 0 ′-Z 7 ′. The task of an inventive sorter is to sort these three bits in an appropriate manner for efficient addition. Since, in the case of addition, only the number of bits which have been set is relevant but not their position at the inputs of an adder, the eight combinations Z 0 ′-Z 7 ′ may be mapped to only four relevant combinations Z 0 -Z 3  that are equivalent for the purposes of summation. The number of possible states for three bits to be added is thus reduced from eight to four. 
   The task of a sorter is to provide the bits AQ′, BQ′, CQ′ (which are unsorted at the input) in the form of sorted bits AQ, BQ, CQ at the output. In concrete terms, in the table shown in  FIG. 1 , the sorting operation shifts the bits AQ′, BQ′, CQ′ which have been set at the input “to the left” and shifts bits which have not been set “to the right”. By way of example, the state Z 3 ′, in which AQ′=0, BQ′=1 and CQ′=1, is changed to the sorted state Z 2 , where AQ=1, BQ=1 and CQ=0. The other combinations Z 0 ′-Z 7 ′ may be sorted in a corresponding manner. The fact that only the sorted bits AQ, BQ, CQ are consequently used for further addition makes it possible to design an addition table which is matched to the sorting and in which the number of combinations for the bits to be added is greatly reduced. 
     FIG. 2  shows an inventive addition table for adding seven presorted input bits AQ, BQ, CQ, XQ, YQ, ZQ, NQ of significance w. In accordance with the sorting table shown in  FIG. 1 , the bits AQ, BQ, CQ, XQ, YQ, ZQ, NQ to be added have been presorted into two groups of three comprising AQ, BQ, CQ and XQ, YQ, ZQ. The columns C2Q, C1Q and C0Q contain carry bits of significance 2w. Instead of the carry being conventionally coded into two carry bits of significance 2w and 4w, a format having three carry bits of significance 2w has been chosen. The carry is therefore compatible with the groups of three input bits for an addition of more significance. The sum bit of significance w is labeled SQ. 
   In each row of the table shown in  FIG. 2 , a state corresponds to the seven bits AQ, BQ, CQ, XQ, YQ, ZQ, NQ of significance w that are to be added and also to the corresponding addition result SQ, C0Q, C1Q, C2Q. As shown in the addition table, the carry bits C0Q, C1Q, C2Q of significance 2w are also present in presorted form, that is to say carry bits which have been set are on the left and those which have not been set are on the-right. Since both the three first bits AQ, BQ, CQ to be added and the three second bits XQ, YQ, ZQ to be added are present in presorted form, only 32 states or combinations need to be taken into account for the addition. If there were seven bits to be added which had not been presorted, 2 7 =128 combinations of input bits would have to be taken into account. 
   The sorting scheme in accordance with which the three first bits AQ, BQ, CQ of significance w that are to be added, the three second bits XQ, YQ, ZQ of significance w that are to be added and the carry bits C0Q, C1Q and C2Q have been sorted can also be described in such a manner that the same logic states are present for at least two adjacent bits in the groups of three bits AQ, BQ, CQ; XQ, YQ, ZQ; C0Q, C1Q, C2Q. 
   Reducing the possible combinations of input bits AQ, BQ, CQ, XQ, YQ, ZQ, NQ of significance w that are to be added means that, in a circuit implementation of the addition table shown in  FIG. 2 , only a maximum of five transistors or five controlled paths of controllable switches are arranged in series in a critical path, that is to say between an input and an output to which the carry bits C0Q, C1Q, C2Q or the sum bit SQ is/are applied. 
     FIG. 3  shows a block diagram of the inventive adding device  2  for adding seven bits AQ′, BQ′, CQ′, XQ′, YQ′, ZQ′, NQ of equal significance w, the first six bits AQ′, BQ′, CQ′, XQ′, YQ′, ZQ′ of significance w that are to be added being presorted according to the invention by a sorter  3 . 
   The sorter  3  has two sorters  4 ,  5 , each having three inputs  111 - 116  for respectively receiving three of the bits AQ′, BQ′, CQ′; XQ′, YQ′, ZQ′ to be added, and supplies sorted bits at the outputs  117 - 122 , the first three outputs  117 ,  118 ,  119  being parts of the first sorter  4  and supplying the first three presorted bits AQ, BQ, CQ. The second three outputs  120 ,  121 ,  122  are parts of the second sorter  5  and supply the second three presorted bits XQ, YQ, ZQ. 
   The outputs  117 - 122  of the sorters  4 ,  5  are coupled to the inputs  101 - 106  of the adder. The bits AQ, BQ, CQ, XQ, YQ, ZQ, NQ to be added which have been presorted according to the invention are applied to the inputs  101 - 107  of an inventive adder  1  which supplies the sum bit from the addition SQ and three carry bits C0Q, C1Q, C2Q of significance 2w at four outputs  11 - 14 . 
   The carry bits at the outputs  12 - 14  for the carry bits C0Q, C1Q, C2Q have already been sorted in accordance with the addition table shown in  FIG. 2 . 
     FIG. 4  shows a block diagram of an inventive sorter  4 . The sorter has three inputs  111 ,  112 ,  113  to which three unsorted bits AQ′, BQ′, CQ′ of the seven bits to be added are applied. The three sorted bits AQ, BQ, CQ to be added are applied to the three outputs  117 ,  118 ,  119  of the sorter  4 . The sorter  4  has three circuit blocks  4 - 1 ,  4 - 2 ,  4 - 3  which each have three inputs  111 ′,  112 ′,  113 ′;  111 ″,  112 ″,  113 ″;  111 ′″,  112 ′″,  113 ′″ and are coupled to the inputs  111 ,  112 ,  113  of the sorter  4 , with the result that the three unsorted bits AQ′, BQ′, CQ′ to be added are applied to each circuit block  4 - 1 ,  4 - 2 ,  4 - 3 . Each of the circuit blocks  4 - 1 ,  4 - 2 ,  4 - 3  has an output  117 ′,  118 ″,  119 ′″, the output  117 ′ of the first circuit block  4 - 1  supplying the first sorted bit AQ to the output of the sorter, the second output  118 ″ of the second circuit block  4 - 2  supplying the second sorted bit BQ to the output  118  of the sorter  4 , and the third output  119 ′″ of the third circuit block  4 - 3  supplying the third sorted bit CQ to the output  119  of the sorter  4 . 
     FIG. 5   a  shows a preferred embodiment of the first circuit block  4 - 1  of the sorter;  FIG. 5   b  shows the second circuit block  4 - 2  of the sorter  4 , and  FIG. 5   c  shows the third circuit block  4 - 3  of the sorter  4 . The three circuit blocks  4 - 1 ,  4 - 2 ,  4 - 3  of the sorter  4  have a number of controllable switches and logic inverter stages which are connected to one another as shown in the circuits in  FIGS. 5   a - c.    
     FIG. 6  shows a block diagram of the inventive adder  1  having seven inputs  101 - 107  to which the seven presorted bits AQ, BQ, CQ, XQ, YQ, ZQ, NQ to be added are applied, an output  11  for outputting the sum bit SQ and three outputs  12 ,  13 ,  14  for outputting the carry bits C0Q, C1Q, C2Q. The inventive adder  1  also has four circuit blocks  1 - 1 ,  1 - 2 ,  1 - 3 ,  1 - 4  which are each coupled to the seven inputs  101 - 107 , with the result that the seven sorted bits AQ, BQ, CQ, XQ, YQ, ZQ, NQ to be added are applied to each circuit block. The first circuit block  1 - 1  supplies the sum bit SQ to the output  11  of the adder. The second circuit block  1 - 2  supplies the first carry bit C0Q to the output  14 , the third circuit block  1 - 3  supplies the second carry bit C1Q to the output  13  and the fourth circuit block supplies the third carry bit C2Q to the output  12  of the adder  1 .  FIGS. 7   a - d  show preferred embodiments of the circuit blocks  1 - 1 ,  1 - 2 ,  1 - 3 ,  1 - 4  of the adder. 
   The circuit arrangements  1 - 1 ,  1 - 2 ,  1 - 3 ,  1 - 4  of the circuit blocks in the adder  1  have a multiplicity of controllable paths and inverter stages which are connected to one another in accordance with the circuits shown in  FIGS. 7   a - d.  In this case, the reference symbols A, B, C, N, X, Y, Z, S, C 0 , C 1 , C 2  denote the inverted signals corresponding to the references AQ, BQ, CQ, NQ, XQ, YQ, ZQ, SQ, C0Q, C1Q, C2Q. It will be understood that the inverted signals are generated by interposing inverter stages. In the circuit implementation of the inventive adder  1  shown in  FIGS. 7   a - d,  there are a maximum of five controllable paths between one of the outputs  11 - 14  and a supply connection VDD, VSS. As a result of this particularly low number of controlled paths of controllable switches, the preferred embodiment of the inventive adder  1  is particularly fast and has a low power consumption. 
   Although the present invention has been described above with reference to a particular embodiment, it is not restricted thereto but rather can be modified multifariously. 
   The invention is thus not restricted to the special circuit design of the sorting circuit or adder shown above figures. Rather, just this circuit arrangement can be modified without departing from the fundamental principle of the invention. In particular, other circuit implementations of the addition table shown in  FIG. 2  are conceivable.