Binary / Decimal / Hex Converter
Convert numbers between binary, decimal, and hexadecimal instantly.
Enter any value in any base to see all three conversions with optional octal output.
Binary is base-2 — a number system that uses only two digits, 0 and 1. It’s the native language of computers, which represent all data as combinations of on (1) and off (0) electrical signals. Converting between binary and decimal is a fundamental skill in computer science and digital electronics.
Binary to Decimal conversion: Decimal = Σ (Bit × 2ⁿ)
Each bit position represents a power of 2, starting from 2⁰ at the rightmost position.
Worked example: Binary: 1101 1010
Position values (right to left): 2⁷ 2⁶ 2⁵ 2⁴ 2³ 2² 2¹ 2⁰ = 128, 64, 32, 16, 8, 4, 2, 1
Calculation: (1×128) + (1×64) + (0×32) + (1×16) + (1×8) + (0×4) + (1×2) + (0×1) = 128 + 64 + 0 + 16 + 8 + 0 + 2 + 0 = 218
Decimal to Binary conversion: Divide the number by 2 repeatedly, recording remainders. Read remainders bottom to top.
Example: Convert 218 to binary 218 ÷ 2 = 109 R 0 109 ÷ 2 = 54 R 1 54 ÷ 2 = 27 R 0 27 ÷ 2 = 13 R 1 13 ÷ 2 = 6 R 1 6 ÷ 2 = 3 R 0 3 ÷ 2 = 1 R 1 1 ÷ 2 = 0 R 1 Read remainders upward → 1101 1010 ✓
Quick reference — common values:
- 0000 = 0 | 0001 = 1 | 0010 = 2 | 0100 = 4 | 1000 = 8
- 1111 = 15 | 1111 1111 = 255 (one byte, max)
- One byte = 8 bits | Kilobyte ≈ 1,024 bytes | Megabyte ≈ 1,048,576 bytes