A bit slice multiplication circuit operating to slice a multiplier, produce products for the sliced multipliers and a multiplicand and sum the products to obtain the multiplication result. The circuit includes a slicing unit for slicing the multiplicand, multiplying units corresponding in number to the number of sliced multiplicands, and adding units provided in correspondence to the multiplying units and implementing summation for multiplication results from corresponding multiplying units while shifting the sliced portions of the multiplicand at each multiplying operation for sliced multipliers and multiplicands by the multiplying units, the multiplication result being obtained by summing all summation results produced by the adding units.

High and low order bit carry propagation adders are connected to outputs of carry save adder trees which produce half-sums and half-carries. Following carry propagation addition of the low order bits carry propagation addition of the high order bits is carried out. A carry from the low order bit carry propagation addition is added to the high order bit carry propagation addtion.

A method nad circuitry for multiplication in a digital system is described. The circuitry includes a partial product generator, a carry-save adder, a sum latch, a carry latch, an adder, a latch, circuitry for truncating, and coupling circuitry. A method and circuitry for optimizing a speed of a subsequent multiplication in a digital system is described. Circuitry for optimizing multiplication clock cycles in a digital system is described.

A sum-of-products calculating circuit includes a bit extension circuit, wherein the most significant bit of an intermediate result of the multiplication effected by a multiplier is extended from an order one bit of the order higher than that of the most significant bit of the intermediate result of the multiplication to the sign bit of addition input data to an adder, by using the most significant bit of each of two intermediate results of the multiplication effected by a multiplier and the sign bit of each of multiplication input data to the multiplier. The data having the extended data bits are inputted to an adder as addition data for the addition performed therein. Thereby, the number of bits used for representing output data of the multiplier can be equalized with that of bits used for representing input data of the adder by a simple logic circuit without the addition of dummy bits to the addition data. Thus, the component elements of the calculating circuit is substantially reduced in number.

A partial product adder for summing up four partial products P0, P1, P2, and P3 which are binary numbers in twos-complement representation having different weights is composed of a carry save adder consisting of an array of 4:2 compressors each having four inputs. Of the four inputs of each 4:2 compressor, the input W presents the shortest propagation delay, while the inputs Y and Z compose critical paths. To implement sign extension of the first partial product P0 having the smallest weight, a logic circuit provides, in a plurality of digit positions higher than the sign digit P0s of the first partial product, values resulting from a logic operation between the value of the sign digit P0s of the first partial product and the value of the sign digit P1s of the second partial product having the second smallest weight. The first partial product P0 after sign extension is allocated to the input W of the carry save adder, while the plurality of upper digits of the input Z related to the second partial product P1 have their values fixed to 0. This reduces a time penalty accompanying the sign extension.