Developer / IT · Number Systems
Binary & Hex Calculator — Arithmetic, Bitwise AND/OR/XOR & Shifts
Do arithmetic and bitwise operations directly in binary, octal, decimal or hexadecimal: +, −, ×, integer ÷ with remainder, AND, OR, XOR, NOT and left/right shifts. See the answer in all four bases, grouped for reading, and pick an 8-, 16-, 32- or 64-bit width to see two's complement and overflow.
Also listed inMathematics
Your inputs
Quick start — try a typical case
With a width, negative results are shown in two's complement and overflow is flagged.
Your result Live
Result (binary)
1 0010 0011
291 in decimal
- Binary
- 1 0010 0011
- Octal
- 443
- Decimal
- 291
- Hexadecimal
- 123
How this is calculated
Arithmetic as in decimal, carrying in the chosen base · AND/OR/XOR bit by bit · A << n = A × 2ⁿ · A >> n = ⌊A ÷ 2ⁿ⌋ · two's complement: −x = 2ʷ − x
- w
- Bit width
Binary arithmetic works like decimal, but you carry at 2 instead of 10: 1 + 1 = 10. Bitwise operations compare the numbers bit by bit — AND keeps bits set in both, OR in either, XOR in exactly one. Shifting left by n multiplies by 2ⁿ. Computers store negative numbers in two's complement: in 8 bits, −1 is 1111 1111.
Assumptions & sources
- Integers only. Division truncates toward zero; the remainder has the sign of A.
- Right shifts of negative numbers are arithmetic (the sign is kept).
- 1Number systems and binary arithmetic — NCERT Computer Science, Class 11 — Encoding Schemes and Number System
Calculator ID DEV-BINARY-001 · version 1.0.0
Common questions
What is 1011 + 0110 in binary?
10001 (11 + 6 = 17).
What does XOR do?
Each result bit is 1 when exactly one of the two input bits is 1: 1100 XOR 1010 = 0110.
How is −5 stored in 8 bits?
As 1111 1011 in two's complement: 256 − 5 = 251.