---
title: "Signed 1's complement addition of (-65)+(+15)"
subject: "Digital Logic"
chapter: 5
key: "semester_3/digital_logic:ones-complement-addition-8bit"
source: https://www.bctengineer.com/q/semester_3/digital_logic/ones-complement-addition-8bit
site: BCT Engineering
---

# Signed 1's complement addition of (-65)+(+15)

Digital Logic · Chapter 5: Arithmetic Circuits

- Asked in: 2081 Bhadra, 3 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/ones-complement-addition-8bit
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-5

## Question

Perform addition of (-65) and (+15) using signed 1's complement representation with the 8-bit format.

## Short answer

Represent -65 as 10111110 and +15 as 00001111. Add: 10111110 + 00001111 = 11001101. No end-around carry. The result is negative; its magnitude is 00110010 = 50, so the sum is -50.

## Answer

In signed 1's complement form a negative number is the 1's complement (all bits inverted) of its positive value; the MSB is the sign bit. An end-around carry, if produced, is added back to the LSB.

**Step 1: Represent the numbers in 8 bits**

$$
\begin{aligned} +65 &= 0100\,0001 \\ -65 &= 1011\,1110 \quad (\text{1's complement}) \\ +15 &= 0000\,1111 \end{aligned}
$$

**Step 2: Add**

```text
   1011 1110   (-65)
 + 0000 1111   (+15)
 -----------
   1100 1101
```

There is **no end-around carry** out of the MSB, so the result is already in final form. The sign bit is 1, so the result is **negative** and is in 1's complement form.

**Step 3: Find the magnitude**

$$
\overline{1100\,1101} = 0011\,0010 = 32 + 16 + 2 = 50
$$

**Answer:** $(-65) + (+15) = 1100\,1101$ in 8-bit signed 1's complement, which is $-50$. Check: $-65 + 15 = -50$. No overflow, because the operands have opposite signs.

## Check yourself

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

1. How is -65 represented in 8-bit signed 1's complement?
   A. 1011 1110 (invert all bits of 0100 0001)
   B. 1011 1111
   C. 1100 0001
   D. 0100 0001
   Answer: A. 1's complement means inverting every bit of +65. (Key point: Negative representation)

2. What is done with a carry out of the MSB in 1's complement addition?
   A. It is discarded
   B. It is added back to the LSB
   C. It is added to the sign bit
   D. It is complemented
   Answer: B. This end-around carry correction is required; here none occurred. (Key point: End-around carry)

3. What is (-65) + (+15) in this representation?
   A. 1100 1101, which is +50
   B. 0011 0010, which is -50
   C. 1100 1101, which is -50
   D. 1101 1110, which is -35
   Answer: C. Sum 1100 1101 has sign 1; its complement 0011 0010 = 50 so it is -50. (Key point: Result)

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