Question

Subtract (10110), from (110110) using the two's complement method.​

Answer 1

Answer:

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The numbers of bits in the subtrahend is 5 while that of minuend is 6. We make the number of bits in the subtrahend equal to that of minuend by taking a `0’ in the sixth place of the subtrahend.

Now, 2’s complement of 010110 is (101101 + 1) i.e.101010. Adding this with the minuend.

1 1 0 1 1 0 Minuend

1 0 1 0 1 0 2’s complement of subtrahend

Carry over 1 1 0 0 0 0 0 Result of addition

After dropping the carry over we get the result of subtraction to be 100000.

(ii) 10110 – 11010

Solution:

2’s complement of 11010 is (00101 + 1) i.e. 00110. Hence

Minued - 1 0 1 1 0

2’s complement of subtrahend - 0 0 1 1 0

Result of addition - 1 1 1 0 0

As there is no carry over, the result of subtraction is negative and is obtained by writing the 2’s complement of 11100 i.e.(00011 + 1) or 00100.

Hence the difference is – 100.

(iii) 1010.11 – 1001.01

Solution:

2’s complement of 1001.01 is 0110.11. Hence

Minued - 1 0 1 0 . 1 1

2’s complement of subtrahend - 0 1 1 0 . 1 1

Carry over 1 0 0 0 1 . 1 0

After dropping the carry over we get the result of subtraction as 1.10.

(iv) 10100.01 – 11011.10

Solution:

2’s complement of 11011.10 is 00100.10. Hence

Minued - 1 0 1 0 0 . 0 1

2’s complement of subtrahend - 0 1 1 0 0 . 1 0

Result of addition - 1 1 0 0 0 . 1 1

As there is no carry over the result of subtraction is negative and is obtained by writing the 2’s complement of 11000.11.

Hence the required result is – 00111.01.

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Answer 2

Answer:

Subtract (10110), from (110110) using the two's complement method.