On Determination of Optimal Distributions of Carry Skips in Adders

The methods for determining the carry skip distributions in the adders with the minimum carry propagation time and the minimum number of carry skip circuits for a given carry propagation time are presented on the assumption that every adder position is comprised either in one skip at most or in two skips at most. Two types of adders with carry skips and each of them without and with end-around-carry are considered. The first one is a classical type of adder composed of identical one-position adders, the second is a NOR-gate adder containing 6 NOR-gates for one adder position only, and 1 NOR-gate for one position of the carry line only. These numbers of gates in the adder result in its economical advantages and relatively small carry propagation time as compared with many other adders. The presented skip distributions demand a relatively small number of skips and give a significant reduction in the carry propagation time.