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What shall be the 2’s complement represented of -24 in a 16 bit computer?
1. 1111 1111 1110 1011
2. 1111 1111 1110 1001
3. 1111 1111 1110 0111
4. 1111 1111 1110 1000

1 Answer

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Correct Answer - Option 4 : 1111 1111 1110 1000

Option 1:

Since 1111 1111 1110 1011 is in 2’ complement number system it can be written as 101011

Decimal of this binary -32 x 1 + 16 x 0 + 8 x 1 + 4 x 0 + 2 x 1 + 1 x 1 = -32 + 8 + 2 + 1 = -21

Option 2:

Since 1111 1111 1110 1001 is in 2’ complement number system it can be written as 10 1001

Decimal value of above binary: -32 x 1+ 16 x 0 + 8 x 1 + 4 x 0 + 2 x 0 + 1 x 1 = -32 + 8 + 1 = -23

Option 3:

Since 1111 1111 1110 0111 is in 2’ complement number system it can be written as 10 0111

Decimal value of above binary: -32 x 1 + 16 x 0 + 8 x 0 + 4 x 1 + 2 x 1 + 1 x 1 = -32 + 4 + 2 + 1 = -25

Option 4:

Since 1111 1111 1110 1000 is in 2’ complement number system it can be written as 101000

Decimal value of above binary: -32 x 1 + 16 x 0 + 8 x 1 + 0 + 0 + 0 = -32 + 8 = -24

Therefore option 4 is the correct answer.

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