Efficient implementation of 3X for radix-8 encoding

Several commercial processors have selected the radix-8 multiplier architecture to increase their speed, thereby reducing the number of partial products. Radix-8 encoding reduces the digit number length in a signed digit representation. Its performance bottleneck is the generation of the term 3X, also referred to as hard multiple. This term is usually computed by an adding and shifting operation, 3X=2X+X, in a high-speed adder. In a 2X+X addition, close full adders share the same input signal. This property permits simplified algebraic expressions associated to a 3X operation other than in a conventional addition. This paper shows that the 3X operation can be expressed in terms of two signals, H_i and K_i, functionally equivalent to two carries. H_i and K_i are computed in parallel using architectures which lead to an area- and speed-efficient implementation. For the purposes of comparison, implementation based on standard cells of conventional adders has been compared with the proposed circuits based on these H_i and K_i signals. As a result, the delay of the proposed serial scheme is reduced by roughly 67% without additional cost in area, the delay and area of the carry look-ahead scheme is reduced by 20% and 17%, and that of the parallel prefix scheme is reduced by 26% and 46%, respectively.