Short answer
A binary calculator works on base-2 numbers inside a fixed register of 8, 16, 32 or 64 bits. Enter two binary operands, choose an operation, and read the result in binary, decimal and hex. A result too big for the register overflows and is truncated.
1. Step by step
- 1Pick a word size: 8, 16, 32 or 64 bits.
- 2Enter operand A and operand B using only 0 and 1.
- 3Choose an operation: add, subtract, multiply, divide, a bitwise gate (AND, OR, XOR, NOT, NAND, NOR), a shift or rotate, or two's complement.
- 4Read the result in binary, unsigned decimal and hex, plus the bit-by-bit view.
2. Example: 1011 + 0110
11 + 6 = 17, shown at 8 bits as 00010001 with no overflow.
3. What overflow means
Registers hold a fixed number of bits. At 8 bits, 11111111 + 00000001 would be 256, which needs 9 bits, so the result is truncated to 00000000 and flagged as overflow. A subtraction with a negative answer, such as 0011 − 0101, wraps to 11111110.
| Word size | Unsigned range |
|---|---|
| 8-bit | 0 to 255 |
| 16-bit | 0 to 65,535 |
| 32-bit | 0 to 4,294,967,295 |
| 64-bit | 0 to 18,446,744,073,709,551,615 |
4. Bitwise logic
Gates work on each bit pair. 1100 AND 1010 = 1000, because only the leftmost column has two 1s. OR keeps a 1 if either bit is 1, and XOR keeps it only if exactly one is 1.
5. Shifts
A logical left shift by one doubles an unsigned value as long as no 1 bit falls off the end. An arithmetic right shift keeps the sign bit, so it divides a signed value by 2 and rounds down.
6. Next steps
Try the Binary Calculator. For worked arithmetic see binary arithmetic with examples, for negatives see two's complement explained, and for conversions see the binary conversion chart.
7. Frequently asked questions
What is a binary calculator?expand_more
A tool that does arithmetic and bitwise operations on base-2 numbers, usually inside a fixed word size such as 8 or 32 bits.
What does overflow mean?expand_more
The true result needs more bits than the register has, so the extra high bits are dropped.
Can it handle negative numbers?expand_more
Yes, through two's complement, where the top bit is the sign.
Which word sizes are supported?expand_more
8, 16, 32 and 64 bits.
8. Sources
- menu_bookBinary number (Wikipedia)