--- 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: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # 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 Think of a step counter or a game score climbing by one each time. Underneath, it is adding in binary: column by column just like decimal, except 1 + 1 makes 10 in binary. Write 0 and carry 1 into the next column left, lining the numbers up on the right and working left one bit at a time. **Example.** Add 01101101 and 01011010 the slow way, carrying each 1 + 1 forward. The columns build 11000111, which reads as 199. Since 199 sits below 256, the answer still fits in 8 bits. Eight bits hold 256 patterns, 0 to 255, and no more. When an addition passes the limit, the extra bit falls off the end and the stored answer wraps to a small number, and that event is called overflow. The program may then show a wrong-looking answer, so the fix is more bits or a size check first. **Tip.** Always fold the incoming carry into the column before you read it. Most wrong sums come from a carry that was quietly ignored. **Recap.** Add binary leftward with carries, and call it overflow when the answer outgrows its bits. ## 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)