- 2074 Bhadra · 3 marks
2's complement: (1111)2 − (1110)2
Short answer
Take 2's complement of 1111: 0001. Add: 1110 + 0001 = 1111. No carry out, result negative. 2's complement of 1111 is 0001, so 1110 − 1111 = −(0001)₂ = −1.
Subtract (1111)2 from (1110)2 using 2's complement method.
The question asks to subtract (1111)₂ from (1110)₂, that is, to find 1110 − 1111 (14 − 15 = −1), using 4-bit numbers.
Steps
- Find the 2's complement of the subtrahend 1111: 1's complement = 0000, add 1 gives 0001.
- Add it to the minuend: 1110 + 0001 = 1111.
- There is no carry out of the MSB, so the result is negative and is in 2's complement form.
- Find the magnitude: 2's complement of 1111 = 0000 + 1 = 0001.
1110
+ 0001 (2's complement of 1111)
------
1111 no end carry -> result negative
Answer: 1110 − 1111 = −(0001)₂ = −1
✓ Answer checked by Claude Opus 5.5 (high effort)
Related questions
- 2's complement: (1111)2 − (1100)2 · Basic Electronics Engineering, chapter 6
- 2's complement subtraction; AND using NOR · Basic Electronics Engineering, chapter 6
- Gray→BCD, decimal→Excess-3 and 2's complement addition · Digital Logic, chapter 1
- Full adder using decoder; (57−43) by 2's complement · Digital Logic, chapter 4
- DEMUX applications; 010 − 011 by 2's complement · Digital Logic, chapter 4
- FFH AND C0H; (16)₁₀ − (26)₁₀ by 2's complement · Digital Logic, chapter 5