Computer Science · Base-2
Binary
Calculator
Add, subtract, multiply and divide binary numbers. Convert between binary, decimal, hexadecimal, and octal instantly with a built-in reference table.
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Binary
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Decimal
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Hex
Binary Arithmetic
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Binary → Decimal / Hex / Octal
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Decimal → Binary / Hex / Octal
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All Base Conversions
DEC
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📋 Binary Reference Table (0–31)
| Dec | Binary | Hex | Oct | Dec | Binary | Hex | Oct |
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How Binary Numbers Work
Binary is a base-2 number system using only 0 and 1. Every digit (bit) represents a power of 2. It is the foundation of all digital computing.
Conversion Formulas
Binary → Decimal: sum each bit × 2^position
1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13
Decimal → Binary: divide by 2, record remainders
13 → 1101
Binary → Hex: group 4 bits: 1101 0111 = D7
Binary → Oct: group 3 bits: 011 010 111 = 327
Why do computers use binary?
Electronic circuits have two stable states — on (1) and off (0). Binary arithmetic is simple: only four addition rules. All higher operations reduce to binary addition with bit manipulation.
What is a bit, nibble, and byte?
A bit = 1 binary digit. A nibble = 4 bits (one hex digit). A byte = 8 bits (values 0–255). Modern CPUs process 64-bit chunks simultaneously.
How does binary addition work?
Rules: 0+0=0, 0+1=1, 1+0=1, 1+1=0 carry 1. Work right-to-left like decimal addition, carrying when sum exceeds 1.