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 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

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Answer 1

Question

Chapter 2, Problem 43E

a)

Program Plan Intro

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 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)

Expert Solution

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)

Program Plan Intro

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)

Expert Solution

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)

Program Plan Intro

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)

Expert Solution

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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Answer 2

Question

Chapter 2, Problem 43E

a)

Program Plan Intro

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 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)

Expert Solution

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)

Program Plan Intro

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)

Expert Solution

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)

Program Plan Intro

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)

Expert Solution

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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Answer 3

Question

Chapter 2, Problem 43E

a)

Program Plan Intro

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 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)

Expert Solution

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)

Program Plan Intro

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)

Expert Solution

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)

Program Plan Intro

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)

Expert Solution

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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Answer 4

Question

Chapter 2, Problem 43E

a)

Program Plan Intro

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 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)

Expert Solution

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)

Program Plan Intro

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)

Expert Solution

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)

Program Plan Intro

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)

Expert Solution

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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Answer 5

Chapter 2, Problem 43E

a)

Program Plan Intro

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 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)

Expert Solution

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)

Program Plan Intro

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)

Expert Solution

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)

Program Plan Intro

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)

Expert Solution

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 “ $00010100$ ”.

Answer 6

Chapter 2, Problem 43E

a)

Program Plan Intro

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 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)

Expert Solution

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 “ $11100111$ ”.

Answer 7

Chapter 2, Problem 43E

a)

Program Plan Intro

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 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

Answer 8

a)

Expert Solution

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 “ $11100111$ ”.

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

b)

Program Plan Intro

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)

Expert Solution

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 “ $11110001$ ”.

Answer 13

b)

Program Plan Intro

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

Answer 14

b)

Expert Solution

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 “ $11110001$ ”.

Answer 15

b)

Expert Solution

Answer 16

b)

Expert Solution

Answer 17

Expert Solution

Answer 18

c)

Program Plan Intro

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)

Expert Solution

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 “ $00010100$ ”.

Answer 19

c)

Program Plan Intro

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

Answer 20

c)

Expert Solution

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 $11111101$

$00000000 (00 means simple shift) +00000000 (00 means simple shift) + 00000101 (10=subtract 1011= add 00000101) +00000000 (11 means simple shift)-------------------- 000000010100$