Audio Version available in YouTube Link : www.youtube.com/Aksharam subscribe the channel Computer Architecture and Organization V semester Anna University By Babu M, Assistant Professor Department of ECE RMK College of Engineering and Technology Chennai

1. MODIFIED BOOTH’S ALGORITHM
RADIX – 4 / BIT PAIR RECODING ALGORITHM
Signed Binary Multiplication Algorithm
E.g.: Binary Multiplication of Positive Multiplicand & Negative Multiplier (+13 X -7)

2. EXPLANATION
Binary Multiplication of (+13 X -7)
STEP 1: Number Representation
Multiplicand +13
Multiplier -7
1101
1110
0
1
Binary Representation 2’s Compliment Representation
01101
11001

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

4. BINARY MULTIPLICATION OF (+13 X -7)
STEP 3: Multiplication
Multiplicand 01101
Recoded Multiplier 0 -2 +1
Note:
1. Multiplication with 0 – 0 (00000)
2. Multiplication with +1 – Multiplicand (01101)
3. Multiplication with -1 – 2’s compliment of Multiplicand (10011)
4. Multiplication with +2 – Shift Multiplicand left by 1 bit (011010)
5. Multiplication with -2 – 2’s compliment of Shifted Multiplicand (100110)
0 1 1 0 1
0 -2 +1
0 1 1 0 10 0 0 0 0
1 0 0 1 1 01 1
0 0 0 0 00
1010010111
11

5. BINARY MULTIPLICATION OF (+13 X -7)
1110100101
+13 -7
01101 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
1110100101
0001011011
2’s Compliment