Convert Decimal to Binary

Convert Decimal (dec) to Binary (bin) instantly and accurately.

Selected Decimal (dec) - available characters: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Conversion Formula

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

Convert Decimal (base 10) → Binary (base 2)

Step 1: Input is already decimal - skip to Step 2.
        Value: 42

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

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Result:  42 (dec) = 101010 (bin)

About Decimal

Decimal (base 10) is the universal positional system using digits 0-9. Each position is a power of 10: 10⁰=1, 10¹=10, 10²=100. Attributed to human anatomy (ten fingers). The Hindu-Arabic system - including zero - was formalised by Brahmagupta (628 CE) and spread via al-Khwarizmi (c. 820 CE). SI and metric systems are base-10. IEEE 754-2008 added decimal64/128 formats for exact decimal arithmetic in financial applications. Conversion: decimal 42 is the reference value used throughout this converter.

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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