Convert Hexadecimal to Binary

Convert Hexadecimal (hex) to Binary (bin) instantly and accurately.

Selected Hexadecimal (hex) - available characters: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Conversion Formula

Step-by-step example using the value 42 (decimal):

Convert Hexadecimal (base 16) → Binary (base 2)

Step 1: Expand each digit of 2A (hex) by position:

        2 × 16^1 = 32
        A × 16^0 = 10
        ────────────
        Sum = 42 (decimal)

Step 2: Divide 42 by 2 repeatedly (read remainders upward):

        42 ÷ 2 = 21  r 0
        21 ÷ 2 = 10  r 1
        10 ÷ 2 =  5  r 0
         5 ÷ 2 =  2  r 1
         2 ÷ 2 =  1  r 0
         1 ÷ 2 =  0  r 1
        Read remainders upward: 101010

────────────────────────────
Result:  2A (hex) = 101010 (bin)

About Hexadecimal

Hexadecimal (base 16) uses digits 0-9 and A-F (A=10, B=11, C=12, D=13, E=14, F=15). Each position is a power of 16: 16⁰=1, 16¹=16, 16²=256. Because 16 = 2⁴, each hex digit = exactly 4 bits (one nibble). Ubiquitous in computing: memory addresses (0x7FFF…), CSS colours (#FF5733), IPv6, SHA-256 hashes (64 hex digits = 256 bits), MAC addresses, UUID/GUIDs, and binary file magic numbers. The '0x' prefix originated in C (1972) and is standard in C++, Java, Python, JS, Rust, and Go. Conversion: decimal 42 = 2×16+10 = 2A₁₆.

About Binary

Binary (base 2) is the foundational numeral system of all digital electronics, using only 0 and 1. Each position represents a power of 2: 2⁰=1, 2¹=2, 2²=4, 2³=8. Leibniz formalised it in 1679; Shannon applied Boolean logic to circuits in 1948. 8 bits = 1 byte (256 values) - the fundamental unit in every CPU from the 8080 to ARM Cortex-X. Every integer, float, character, pixel, and instruction in any digital device is ultimately binary. Conversion: decimal 42 = 32+8+2 = 2⁵+2³+2¹ = 101010₂.

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