2072 Magh · 2 marks

2's complement: (1111)2 − (1100)2

Short answer

2's complement of 1111 is 0001. 1100 + 0001 = 1101, no carry, result negative. 2's complement of 1101 gives magnitude 0011, so 1100 − 1111 = −(0011)₂ = −3.

Subtract (1111)2 from (1100)2 using 2's complement method.

The question asks to subtract (1111)₂ from (1100)₂, that is, 1100 − 1111 (12 − 15 = −3), using 4 bits.

1's complement of 1111 = 0000; 2's complement = 0000 + 1 = 0001.
Add: 1100 + 0001 = 1101.
No carry is generated, so the answer is negative, and 1101 is the 2's complement of the magnitude.
Magnitude: 1's complement of 1101 = 0010; add 1 gives 0011.

   1100
 + 0001
 ------
   1101   no carry -> negative

Answer: 1100 − 1111 = −(0011)₂ = −3

✓ Answer checked by Claude Opus 5.5 (high effort)

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2's complement: (1111)2 − (1100)2

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