---
title: "2's complement: 42 − 115"
subject: "Basic Electronics Engineering"
chapter: 6
key: "semester_2/basic_electronics_engineering:two-complement-42-115"
source: https://www.bctengineer.com/q/semester_2/basic_electronics_engineering/two-complement-42-115
site: BCT Engineering
---

# 2's complement: 42 − 115

Basic Electronics Engineering · Chapter 6: Digital Electronics

- Asked in: 2070 Bhadra, 2 marks
- 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-42-115
- Whole chapter: https://www.bctengineer.com/md/semester_2/basic_electronics_engineering/chapter-6

## Question

Perform the subtraction using 2's complement method: 42(10) − 115(10)

## Short answer

42 = 00101010, 115 = 01110011 (8-bit). 2's complement of 115 = 10001101. Sum: 00101010 + 10001101 = 10110111, no carry. Magnitude from 2's complement is 01001001 = 73, result −73.

## Answer

We compute 42 − 115 using 8-bit numbers.

- 42 = 00101010
- 115 = 01110011

1. 1's complement of 115 = 10001100; add 1: 2's complement = **10001101**.
2. Add to 42:

```text
   00101010   (42)
 + 10001101   (2's complement of 115)
 ----------
   10110111
```

3. There is no carry out of the MSB, so the result is negative.
4. Magnitude = 2's complement of 10110111 = 01001000 + 1 = 01001001 = 64 + 8 + 1 = 73.

**Answer: 42 − 115 = −73**

## Check yourself

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

1. With 8 bits, the 2's complement of 115 (01110011) is:
   A. 10001101
   B. 10001100
   C. 01110100
   D. 10001110
   Answer: A. The answer states this: 10001101. (Key point: 2's complement of 115)

2. 00101010 + 10001101 equals:
   A. 10110110
   B. 10110111
   C. 11000111
   D. 01001001
   Answer: B. The answer states this: 10110111. (Key point: Sum)

3. No carry out of the MSB means the result is:
   A. Positive
   B. Zero
   C. Negative
   D. Overflowed
   Answer: C. The answer states this: Negative. (Key point: Sign test)

4. 42 - 115 equals:
   A. +73
   B. -157
   C. -72
   D. -73
   Answer: D. The answer states this: -73. (Key point: Final answer)

## Related in Basic Electronics Engineering

- [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
- [2's complement: 15 − 20](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Atwo-complement-15-20) — Basic Electronics Engineering, chapter 6
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