---
title: "2's complement: (1111)2 − (1100)2"
subject: "Basic Electronics Engineering"
chapter: 6
key: "semester_2/basic_electronics_engineering:two-complement-1111-1100"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/two-complement-1111-1100
site: BCT Engineering
---

# 2's complement: (1111)2 − (1100)2

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2072 Magh, 2 marks
- Video: [Subtraction using 2's complement method.](https://www.youtube.com/watch?v=OyZPqrSPmkU) — Engg-Course-Made-Easy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/two-complement-1111-1100
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

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

## 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.

## Answer

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

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

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

**Answer: 1100 − 1111 = −(0011)₂ = −3**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The 2's complement of 1111 is:
   A. 0001
   B. 0000
   C. 1100
   D. 1110
   Answer: A. The answer states this: 0001. (Key point: 2's complement)

2. 1100 + 0001 equals:
   A. 1111
   B. 1101
   C. 1011
   D. 0001
   Answer: B. The answer states this: 1101. (Key point: Sum)

3. The magnitude of 1101 (2's complement) is:
   A. 0010
   B. 1101
   C. 0011
   D. 0001
   Answer: C. The answer states this: 0011. (Key point: Magnitude)

4. 1100 - 1111 equals:
   A. +3
   B. -2
   C. -15
   D. -3
   Answer: D. The answer states this: -3. (Key point: Result)

## Related in Basic Electronics Engineering

- [2's complement: (1111)2 − (1110)2](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Atwo-complement-1111-1110) — Basic Electronics Engineering, chapter 6
- [2's complement subtraction; AND using NOR](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Atwo-complement-111-110-nor-and) — Basic Electronics Engineering, chapter 6

## Related in other subjects

- [Full adder using decoder; (57−43) by 2's complement](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Afull-adder-decoder-subtract) — Digital Logic, chapter 4
- [DEMUX applications; 010 − 011 by 2's complement](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ademux-applications-subtract) — Digital Logic, chapter 4
- [FFH AND C0H; (16)₁₀ − (26)₁₀ by 2's complement](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ahex-and-twos-complement-subtract) — Digital Logic, chapter 5