Binary Addition
Binary addition carries when the sum is 2.
About this topic
Binary addition works like decimal addition, but there are only four basic cases: 0 plus 0 is 0, 0 plus 1 is 1, 1 plus 0 is 1, and 1 plus 1 is 10, meaning 0 with a carry of 1. Adding from right to left and carrying whenever a column reaches 2 gives the answer.
For example, add 0110 (6) and 0011 (3). The rightmost column is 0 plus 1, which gives 1. Next is 1 plus 1, which gives 0 carry 1. Then 1 plus 0 plus the carry gives 0 carry 1. The final column is 0 plus 0 plus the carry, which gives 1. The result is 1001, or 9, which is correct. Circuits called half adders and full adders do exactly this using logic gates, and chaining them forms the ALU.
If the answer needs more bits than are available, overflow occurs. Adding 1 to 11111111 in an 8-bit register gives 100000000, which loses the ninth bit. Overflow bugs have caused real failures, such as the Ariane 5 rocket crash. A common mistake is forgetting the carry. Always line up the bits and check by converting to decimal.
Key ideas
- 1 + 1 = 10
- Same rules as decimal
- Overflow when out of bits
Quick check
Use cases: where Binary Addition helps
- Homework: review the key idea behind Binary Addition before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Binary Addition without notes.
- Visual learning: play with the interactive lab to see how Binary Addition changes when you adjust its inputs.
- Teaching a friend: explain Binary Addition in your own words, then compare your version with the key ideas.
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Frequently asked questions
What is Binary Addition?
Binary addition carries when the sum is 2.
What will I learn in Binary Addition?
1 + 1 = 10. Same rules as decimal. Overflow when out of bits.
Is Binary Addition part of Computer Science?
Yes. It is one of 80 Computer Science topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Binary Addition lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Binary Addition?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.