---
title: "2's complement: (1111)2 − (1110)2"
subject: "Basic Electronics Engineering"
chapter: 6
key: "semester_2/basic_electronics_engineering:two-complement-1111-1110"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/two-complement-1111-1110
site: BCT Engineering
---

# 2's complement: (1111)2 − (1110)2

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2074 Bhadra, 3 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-1111-1110
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

Subtract (1111)2 from (1110)2 using 2's complement method.

## 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.

## Answer

The question asks to subtract (1111)₂ from (1110)₂, that is, to find 1110 − 1111 (14 − 15 = −1), using 4-bit numbers.

**Steps**
1. Find the 2's complement of the subtrahend 1111: 1's complement = 0000, add 1 gives **0001**.
2. Add it to the minuend: 1110 + 0001 = **1111**.
3. There is no carry out of the MSB, so the result is negative and is in 2's complement form.
4. Find the magnitude: 2's complement of 1111 = 0000 + 1 = 0001.

```text
   1110
 + 0001   (2's complement of 1111)
 ------
   1111   no end carry -> result negative
```

**Answer: 1110 − 1111 = −(0001)₂ = −1**

## 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. 1110
   D. 1111
   Answer: A. The answer states this: 0001. (Key point: Subtrahend complement)

2. 1110 + 0001 equals:
   A. 0000
   B. 1111
   C. 1101
   D. 10000
   Answer: B. The answer states this: 1111. (Key point: Addition result)

3. No carry out of the MSB means:
   A. The result is positive
   B. An overflow error
   C. The result is negative and in 2's complement form
   D. The result is zero
   Answer: C. The answer states this: The result is negative and in 2's complement form. (Key point: Meaning of no carry)

4. 1110 - 1111 equals:
   A. +1
   B. -15
   C. -14
   D. -1
   Answer: D. The answer states this: -1. (Key point: Final answer)

## Related in Basic Electronics Engineering

- [2's complement: (1111)2 − (1100)2](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Atwo-complement-1111-1100) — 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

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- [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
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