
a)
Booth’s
- The main goal of booths algorithm is to multiply two signed binary numbers by involving two’s complement notation.
- There are multiple methods available for fast multiplication but those methods will not be applicable for signed multiplication.
- The advantage of booth’s algorithm is not only performs multination faster but also it is efficient to do multiplication on the signed numbers.
Booth’s algorithm reads the value as follows:
- Subtraction of multiplicand takes pace when the multiplier’s current and the preceding bits are 1 and 0 respectively.
- Addition of multiplicand takes pace when the multiplier’s current and the preceding bits are 0 and 1 respectively.
- Left shifting of multiplicand takes pace when the multiplier’s current and the preceding bits are 0 and 0 or 1 and 1 respectively
a)

Explanation of Solution
Multiplying two numbers:
1011(-5)×0101(5)---------------
Since both the numbers are given in 4-bit two’s complement the resultant value should 8-bit which is also in two’s complement.
The multiplicand is “-5”, so the 2’s complement is 0101. The 4-bit value should be extended to 8-bit 00000101
00000101 (10=subtract 1101=add 00000011) +11111011 (01=add 11111011 to product) + 00000101 (10=subtract 1101=add 00000101) +11111011 (01=add 11111011 to product)-------------------- 100111100111
Discard the last 4 bits because only 8 rightmost bits should be considered.
Hence, the resultant will be “11100111”.
b)
Booth’s algorithm:
- The main goal of booths algorithm is to multiply two signed binary numbers by involving two’s complement notation.
- There are multiple method available for fast multiplication but those methods will not be applicable for signed multiplication.
- The advantage of booth’s algorithm is not only performs multination faster but also it is efficient to do multiplication on the signed numbers.
Booth’s algorithm reads the value as follows:
- Subtraction of multiplicand takes pace when the multiplier’s current and the preceding bits are 1 and 0 respectively.
- Addition of multiplicand takes pace when the multiplier’s current and the preceding bits are 0 and 1 respectively.
- Left shifting of multiplicand takes pace when the multiplier’s current and the preceding bits are 0 and 0 or 1 and 1 respectively
b)

Explanation of Solution
Multiplying two numbers
0011(3)×1011(-5)---------------
Since both the numbers are given in 4-bit two’s complement the resultant value should 8-bit which is also in two’s complement.
The multiplicand is “-5”, so the 2’s complement is 0101. The 4-bit value should be extended to 8-bit 00000101
11111101 (10=subtract 0011=add 11111101) +00000000 (11 means simple shift) + 00000011 (01 means 0011) +11111101 (10=subtract 0111= add 11111011)-------------------- 100011110001
Discard the last 4 bits because only 8 rightmost bits should be considered.
Hence, the resultant will be “11110001”.
c)
Booth’s algorithm:
- The main goal of booths algorithm is to multiply two signed binary numbers by involving two’s complement notation.
- There are multiple method available for fast multiplication but those methods will not be applicable for signed multiplication.
- The advantage of booth’s algorithm is not only performs multination faster but also it is efficient to do multiplication on the signed numbers.
Booth’s algorithm reads the value as follows:
- Subtraction of multiplicand takes pace when the multiplier’s current and the preceding bits are 1 and 0 respectively.
- Addition of multiplicand takes pace when the multiplier’s current and the preceding bits are 0 and 1 respectively.
- Left shifting of multiplicand takes pace when the multiplier’s current and the preceding bits are 0 and 0 or 1 and 1 respectively
c)

Explanation of Solution
Multiplying two numbers
1011(-5)×1100(-4)---------------
Since both the numbers are given in 4-bit two’s complement the resultant value should 8-bit which is also in two’s complement.
The multiplicand is “-5”, so the 2’s complement is 1101. The 4-bit value should be extended to 8-bit 11111101
00000000 (00 means simple shift) +00000000 (00 means simple shift) + 00000101 (10=subtract 1011= add 00000101) +00000000 (11 means simple shift)-------------------- 000000010100
Discard the last 4 bits because only 8 rightmost bits should be considered.
Hence, the resultant will be “00010100”.
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Chapter 2 Solutions
Essentials of Computer Organization and Architecture
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