Binary Calculator
Convert and calculate with binary numbers.
Number System Converter
Enter a whole number (0-999999)
Number System Reference
Decimal
Base 10
Binary
Base 2
Octal
Base 8
Hexadecimal
Base 16
Binary Details
Common Conversions
How it works
Binary is base-2: every digit is a power of two, using only 0 and 1. This calculator converts between binary and decimal and does binary arithmetic. To read a binary number, add up the place values where there's a 1.
Binary to decimal
Decimal = Σ (digit × 2^position) counting positions from 0 on the right
- digit
- 0 or 1
- 2^position
- place value (1, 2, 4, 8, 16, …)
Worked example
- Convert binary 1011 to decimal
- 1×8 + 0×4 + 1×2 + 1×1
1011₂ = 11 in decimal.
Good to know
- Each binary digit is a 'bit'; eight bits make a byte (values 0–255).
- Binary is how computers store everything — text, numbers, and images all reduce to bits.
- Adding in binary carries at 2 (1 + 1 = 10), just as decimal carries at 10.
Related Calculators
Frequently Asked Questions
What is binary?
Binary is base-2 numbering using only 0 and 1 — the fundamental language of computers, where each digit (bit) represents an on/off state. Every place value is a power of two: 1, 2, 4, 8, 16, and so on.
How do I convert decimal to binary?
Repeatedly divide by 2 and record the remainders, then read them from bottom to top. For 13: 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1 — so 13 is 1101 in binary.
How do I add binary numbers?
Column by column, just like decimal, except you carry at 2 instead of 10: 1 + 1 = 10 (write 0, carry 1). For example, 1011 + 0110 = 10001, which is 11 + 6 = 17 in decimal.
What are bitwise operations?
Operations applied to individual bits: AND (&), OR (|), XOR (^), NOT (~), and shifts (<<, >>). They are essential in low-level programming for flags, masks, and fast arithmetic — a left shift by one doubles a number.
What are bits, bytes, and hexadecimal?
A bit is one binary digit; eight bits make a byte, which holds values 0-255. Hexadecimal (base-16) is shorthand for binary — each hex digit encodes exactly four bits, so a byte is two hex digits, like FF for 11111111.