Modified booth's algorithm Part 2

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Computer Architecture and Organization
V semester
Anna University
By
Babu M, Assistant Professor
Department of ECE
RMK College of Engineering and Technology
Chennai

1. Signed Binary Multiplication Algorithm E.g.: Binary Multiplication of Negative Multiplicand & Negative Multiplier (-13 X -7) Modified BOOTH’s ALGORITHM RADIX – 4 / Bit pair recoding algorithm

2. Explanation with an example Binary Multiplication of (-13 X -7 ) STEP 1: Number Representation Multiplicand - 13 Multiplier -7 1101 111 1 1 Binary Representation 2’s Compliment Representation 10011 11001

3. Binary Multiplication of (-13 X -7 ) STEP 2: Bit Pair Recoding of the Multiplier Multiplier - 7 11001 1 1 1 Recoded Multiplier Multiplier Multiplicand selected Bit i+1 Bit i Bit i-1 0 X Multiplicand 1 +1 X Multiplicand 1 +1 X Multiplicand 1 1 +2 X Multiplicand 1 -2 X Multiplicand 1 1 -1 X Multiplicand 1 1 -1 X Multiplicand 1 1 1 0 X Multiplicand Modified Booth’s Recoding Table i i-1 +1 i+1 i i-1 i+1 -2 i i-1 i+1 1

4. Binary Multiplication of (-13 X -7 ) STEP 3: Multiplication Multiplicand 10011 Recoded Multiplier 0 -2 +1 Note: 1. Multiplication with 0 – 0 (00000) 2. Multiplication with +1 – Multiplicand (10011) 3. Multiplication with -1 – 2’s compliment of Multiplicand (01101) 4. Multiplication with +2 – Shift Multiplicand left by 1 bit (100110) 5. Multiplication with -2 – 2’s compliment of Shifted Multiplicand (011010) 1 1 1 0 -2 +1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1

5. Binary Multiplication of (-13 X -7 ) 0001011011 - 13 - 7 100 1 1 0 -2 -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