Booth's coding in 8 bits for the decimal number -57 isa)0-100+1000b)0-100+100-1c)0-1+100-10+1d)00-10+100-1Correct answer is option 'B'. Can you explain this answer?

Question

Answer

There are 2 ways for answering This questions.
Way 1 -> Convert 57 to Binary & Get 2's complement. It is "11000111" & Attach one extra 0 to right of it
110001110

To calculate booth code subtract right digit from left digit in every consecutive 2 digits.
So 11-> 0 , 10 -> +1, .. finally 10 -> +1

Answer

Take 2's compliment of -57= 11000111
put 0 at LSB as, 110001110
take pair two symbols from right side encode it as ,
00-> 0
01-> 1
10-> -1
11-> 0

you will get answer as 0 -1 0 0 1 0 0 -1

Answer

Answer:

To represent the decimal number -57 in Booth's coding with 8 bits, we can follow the below steps:

Step 1: Determine the binary representation of the absolute value of the decimal number. In this case, the absolute value of -57 is 57, which can be represented in binary as 111001.

Step 2: Add an extra bit at the leftmost position to represent the sign of the number. If the number is positive, the leftmost bit is set to 0. If the number is negative, the leftmost bit is set to 1. In this case, since the number is negative, the leftmost bit is set to 1.

So, the binary representation of -57 becomes: 1111001.

Step 3: Apply Booth's algorithm to convert the binary representation into Booth's coding.

Starting from the leftmost bit and moving towards the right, we group the consecutive bits into three-bit segments. For each segment, we perform the following operations:

000: No operation required. Leave the bits unchanged.

001: Subtract 1 from the segment.

010: Subtract 2 from the segment.

011: Subtract 3 from the segment.

100: Add 1 to the segment.

101: Add 2 to the segment.

110: Add 3 to the segment.

111: No operation required. Leave the bits unchanged.

Applying the above rules to the binary representation of -57 (1111001), we get:

1. 1111001: No operation required. Leave the bits unchanged.
2. 1110010: Subtract 3 from the segment.
3. 1111001: No operation required. Leave the bits unchanged.

Therefore, the Booth's coding for -57 in 8 bits is 1110010.

Correct answer: Option B (0-100 100-1)

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