Binary Calculator
Perform binary arithmetic and logical operations. Add, subtract, multiply, divide, AND, OR, XOR binary numbers. Convert between binary, decimal, and hex.
= 10 Decimal
= 3 Decimal
Result
1101
Binary
1101
Decimal
13
Hexadecimal
0xD
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Last updated: January 2026
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Frequently Asked Questions
What is binary and why do computers use it?
Binary is a base-2 number system using only 0 and 1. Computers use it because electronic circuits have two states: on (1) and off (0). All digital data—text, images, programs—is ultimately stored in binary.
How do I convert binary to decimal?
Each binary digit represents a power of 2. From right to left: 2⁰=1, 2¹=2, 2²=4, etc. Binary 1011 = 1×8 + 0×4 + 1×2 + 1×1 = 8 + 0 + 2 + 1 = 11 in decimal.
How do I convert decimal to binary?
Divide by 2 repeatedly, noting remainders. For 13: 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1. Read remainders bottom-up: 1101 is decimal 13 in binary.
What are AND, OR, and XOR operations?
AND: both bits must be 1 (1 AND 1 = 1, else 0). OR: at least one bit is 1 (0 OR 0 = 0, else 1). XOR: exactly one bit is 1 (different bits = 1, same = 0). These are fundamental in computing.
How does binary relate to hexadecimal?
Hexadecimal (base-16) is a shorthand for binary. Each hex digit represents 4 binary digits. Binary 1111 = hex F = 15. Binary 10101010 = hex AA. Programmers prefer hex for its compactness.