Binary addition calculator
Binary addition
1010 0001
107 + 54 = 161, which fits in 8 bits.
- In denary
- 107 + 54 = 161
| Carry | 1 | 1 | 1 | 1 | 1 | 1 | |||
|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | ||
| + | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | |
| = | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
Working
- Line the numbers up on the right, padded to 8 bits: 0110 1011 + 0011 0110.
- 1s column: 1 + 0 = 1: write 1.
- 2s column: 1 + 1 = 2 (10 in binary): write 0, carry 1.
- 4s column: 0 + 1 + 1 carried = 2 (10 in binary): write 0, carry 1.
- 8s column: 1 + 0 + 1 carried = 2 (10 in binary): write 0, carry 1.
- 16s column: 0 + 1 + 1 carried = 2 (10 in binary): write 0, carry 1.
- 32s column: 1 + 1 + 1 carried = 3 (11 in binary): write 1, carry 1.
- 64s column: 1 + 0 + 1 carried = 2 (10 in binary): write 0, carry 1.
- 128s column: 0 + 0 + 1 carried = 1: write 1.
- Answer: 1010 0001. Check in denary: 107 + 54 = 161.
Your result
1010 0001. 107 + 54 = 161, which fits in 8 bits.
Practise binary addition
Your mock plan, in three taps
Binary addition works column by column from the right: 1 + 1 = 10, so write 0 and carry 1; 0110 1011 + 0011 0110 = 1010 0001 (107 + 54 = 161).
Questions people ask
What is 1 + 1 in binary?
10, which is 2 in denary. In a column sum you write 0 and carry 1 to the next column on the left. Three 1s make 11: write 1 and carry 1.
What is an overflow error?
It happens when the answer needs more bits than the computer has room for. Adding two 8-bit numbers can give a 9-bit answer, such as 200 + 100 = 300; an 8-bit register keeps only the lower 8 bits, so the stored answer is wrong.
How do I check a binary addition?
Convert each number to denary, add them and convert the total back. If the total is over 255, an 8-bit answer has overflowed.
Do I have to show the carries?
Showing them is the clearest way to earn the method marks and to find your own mistakes. Write each carry small above the next column to the left.
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How we work this out
What it does
Add two or three binary numbers column by column, with every carry shown and overflow spotted.
Two or three binary numbers of up to 8 bits each, as AQA and OCR set them.
Method
- Line the numbers up on the right and add one column at a time, starting with the 1s.
- 0 + 0 = 0, 0 + 1 = 1, 1 + 1 = 10 (write 0, carry 1) and 1 + 1 + 1 = 11 (write 1, carry 1).
- A carry out of the 128s column means the answer needs 9 bits: in an 8-bit register that is an overflow.