# Multiplication by dsp

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Binary Multiplication
• Multiplication is achieved by adding a list of shifted multiplicands according to the digits of the multiplier. • Ex. (unsigned) 11 1011 multiplicand (4 bits) X 13 X 1101multiplier (4 bits) -------------------------33 101 1 11 0000 ______ 1011 143 1011 --------------------10001111 Product (8 bits)
EECC341 - Shaaban
#1 Lec # 3 Winter 2001 12-6-2001

BinaryMultiplication (continued)
• Instead of listing all shifted multiplicands and then adding, we can add each shifted multiplicand to a partial product. The previous un-signed example becomes:
11 x 13 143 1101 x1101 0000 1011 01011 0000 001011 1011 0110111 1011 10001111 multiplicand multiplier partial product shifted multiplicand partial product shifted multiplicand partial product shifted multiplicandpartial product shifted multiplicand product

EECC341 - Shaaban
#2 Lec # 3 Winter 2001 12-6-2001

Two’s-complement Multiplication
• • A sequence of of two’s-complement additions of shiftedmultiplicands except for last step where the shifted multiplicand corresponding to MSB must be negated. Before adding a shifted multiplicand to the partial product, an additional bit is added to the left ofthe partial product using sign extension.

Ex:
-5 x -3 15

1011 x 1101 00000 11011 111011 00000 1111011 11011 11100111 00101 00001111

multiplicand multiplierpartial product shifted multiplicand partial product shifted multiplicand partial product shifted multiplicand partial product shifted and negated multiplicand product EECC341 - Shaaban

EECC341 -Shaaban
#3 Lec # 3 Winter 2001 12-6-2001

• Shift and subtract Example: 19 10011 11 217 1011 11011001 11 1011 107 0101 99 0000 8 1010 0000 10100 1011 10011 1011 1000

Binary Division
quotientdividend shifted divisor reduced dividend shifted divisor reduced dividend shifted divisor reduced dividend shifted divisor reduced dividend shifted divisor remainder
EECC341 - Shaaban
#4 Lec # 3...