---
title: "Adding Binary Numbers and Overflow"
description: "Adding binary numbers column by column with a carry, and what happens when the answer needs more bits than the space it has."
canonical: https://lightmysky.com/learn/computing/adding-binary-numbers-and-overflow-mt_dBS2OoQscq
source: https://lightmysky.com/learn/computing/adding-binary-numbers-and-overflow-mt_dBS2OoQscq.md
retrieved: 2026-11-12
---

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# Adding Binary Numbers and Overflow

Adding binary numbers column by column with a carry, and what happens when the answer needs more bits than the space it has.

Subject: Computing · Area: Computer Systems · Ages 14 to 15
Page: https://lightmysky.com/learn/computing/adding-binary-numbers-and-overflow-mt_dBS2OoQscq

## Ready when they can

- Add two 8-bit binary numbers, carrying correctly
- Spot an addition whose result no longer fits in 8 bits
- Describe what a program shows when a value overflows

## Lesson: Carry the one, watch the edge

Binary addition uses only 0 and 1. Add the rightmost column first, then move left. When a column totals 2, write 0 and carry 1. When two input 1s and an incoming carry total 3, write 1 and carry 1.

A carry always moves one column left. For example, the carry from the ones column joins the twos column before that column is added.

**Example.** Add 01101101 and 01011010 from right to left. The result is 11000111, which is 199 in decimal.

Eight bits make 256 patterns, from 0 through 255. The number 256 needs a ninth bit, so it cannot be stored as an unsigned 8-bit value.

If a result needs a ninth bit but storage is fixed at 8 bits, the low 8 bits remain and the extra carry is discarded. This is overflow. A program may wrap to a small value, report an error, or use a larger number type.

**Example.** 255 is 11111111 in binary. Adding 1 gives 1 00000000. If only eight result bits are kept, the leading 1 is discarded and 00000000 remains.

**Example.** For 1111 + 1, start at the right. Each 1 plus the incoming carry makes 0 and passes a carry left. The final carry creates 10000.

**Recap.** Add from right to left, carry into the next column, and check whether the result needs more bits.

*Original lesson wording, examples, assessment items, and worked steps authored for the P12 computing curriculum.*

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Binary Numbers and Place Value](https://lightmysky.com/learn/computing/binary-numbers-and-place-value-mt_t67akIKBmI)

## Opens up

- [Hexadecimal as Binary Shorthand](https://lightmysky.com/learn/computing/hexadecimal-as-binary-shorthand-mt_OV6PHdnU6N)
- [Logic Circuits That Add and Remember](https://lightmysky.com/learn/computing/logic-circuits-that-add-and-remember-mt_zPgkt6zf-i)