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Fast 65 Bits X 22 Bits Partial Multiplier

IP.com Disclosure Number: IPCOM000101165D
Original Publication Date: 1990-Jul-01
Included in the Prior Art Database: 2005-Mar-16
Document File: 2 page(s) / 62K

Publishing Venue

IBM

Related People

Desrosiers, B: AUTHOR [+2]

Abstract

This article shows how to perform a multiplication of two numbers of 65 bits in 125 ns (4 cyles of 31.25 ns) due to the implementation of an improved 65 x 22 partial multiplier. The multiplier is composed of: 1. The Booth encoder to reduce the 22 bits of the multiplier to 11 Booth terms. 2. The selectors to introduce in the multiplier array the multiplicand multiplied by the Booth terms. 3. The WALLACE tree of full adders to reduce the 13 terms to two partial results. 4. Two temporary registers to store the above partial results.

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Fast 65 Bits X 22 Bits Partial Multiplier

       This article shows how to perform a multiplication of two
numbers of 65 bits in 125 ns (4 cyles of 31.25 ns) due to the
implementation of an improved 65 x 22 partial multiplier.
      The multiplier is composed of:
       1.  The Booth encoder to reduce the 22 bits of the multiplier
to 11 Booth terms.
 2.  The selectors to introduce in the multiplier array the
multiplicand multiplied by the Booth terms.
 3.  The WALLACE tree of full adders to reduce the 13 terms to two
partial results.
4.  Two temporary registers to store the above partial results.

      There are 13 terms because the 2 partial results are also
introduced in the WALLACE tree in order to save an ADD cycle as
explained below.

      The multiply operation leads to adding 33 selected partial
terms in 3 cycles in order to get two final Sum and Carry terms.
These 2 terms are then added by an 88-bit adder in the last cycle.

      The operation reads as follows:

      In cycle 1: the first 11 P terms, the S term and the C
term (initialized to zero in cycle 0) are reduced by the WALLACE tree
to 2 terms S and C as shown below.
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
      PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
        PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
          PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
            PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
              PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
     ...