Convert Binary to Decimal

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

Selected Binary (bin) - available characters: 0, 1

Conversion Formula

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

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

Step 1: Expand each digit of 101010 (bin) by position:

        1 × 2^5 = 32
        0 × 2^4 =  0
        1 × 2^3 =  8
        0 × 2^2 =  0
        1 × 2^1 =  2
        0 × 2^0 =  0
        ────────────
        Sum = 42 (decimal)

Step 2: Target is decimal - Step 1 result is the final answer.

────────────────────────────
Result:  101010 (bin) = 42 (dec)

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.

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.

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