Booth's algorithm part 3
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The document describes Booth's algorithm for binary multiplication, specifically illustrating the multiplication of a negative multiplicand (-13) and a positive multiplier (+7). This process includes representing the numbers in binary, recoding the multiplier, and executing the multiplication steps. The example further emphasizes the verification of the result using 2's complement representation.
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Booth's algorithm part 3
- 1. BOOTH’S ALGORITHM E.g.: Binary Multiplication of Negative Multiplicand & Positive Multiplier (-13 X +7)
- 2. EXPLANATION WITH AN EXAMPLE Binary Multiplication of (-13 X +7) STEP 1: Number Representation Multiplicand -13 Multiplier +7 1101 1110 1 0 Binary Representation 2’s Compliment Representation 10011 00111
- 3. BINARY MULTIPLICATION OF (-13 X +7) STEP 2: Recoding of the Multiplier Multiplier +7 00111 0 0 1 1 1 Recoded Multiplier Multiplier Multiplicand selected Bit i Bit i-1 0 0 0 X Multiplicand 0 1 +1 X Multiplicand 1 0 -1 X Multiplicand 1 1 0 X Multiplicand Booth’s Recoding Table i 0 i-1 -10 i i-1 0 i i-1 +1 i i-1 0 i i-1
- 4. BINARY MULTIPLICATION OF (-13 X +7) STEP 3: Multiplication Multiplicand 10011 Recoded Multiplier 0+100-1 Note: 1. Multiplication with 0 – 0 (00000) 2. Multiplication with +1 – Multiplicand (10011) 3. Multiplication with -1 – 2’s compliment of Multiplicand (01101) 1 0 0 1 1 0 +1 0 0 -1 0 1 1 0 10 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 1 0 0 1 11 1 0 0 0 0 00 1010010111 11
- 5. BINARY MULTIPLICATION OF TWO POSITIVE NUMBERS (-13 X +7) 1110100101 -13 +7 10011 0+100-1 -13 x +7 1 0 1 1 0 1 1 64 32 16 8 4 2 1 64+16+8+2+1 = 91 -91 STEP 4: Verification 1110100101 0001011011 2’s Compliment