Binary to Decimal Converter

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How does binary to decimal conversion work?
Binary to decimal conversion formula
Conversion process
Examples
Binary to decimal conversion table
Frequently Asked Questions

How does binary to decimal conversion work?

The binary system is base 2 and the decimal system is base 10. To convert, multiply each binary digit by the corresponding power of 2 (starting from the right with 2⁰) and add up the results.

Binary to decimal conversion formula

For a binary number of n digits:

D = \sum_{i = 0}^{n - 1} b_{i} \cdot 2^{i}

Where b_i is each binary digit (0 or 1) at position i.

Decimal Number=bn×2n+bn−1×2n−1+…+b1×21+b0×20\text{Decimal Number} = \color{#B91C1C}b_n \color{#111827}\times 2^n + \color{#B91C1C}b_{n-1} \color{#111827}\times 2^{n-1} + \ldots + \color{#B91C1C}b_1 \color{#111827}\times 2^1 + \color{#B91C1C}b_0 \color{#111827}\times 2^0Decimal Number=bn​×2n+bn−1​×2n−1+…+b1​×21+b0​×20

Conversion process

Write the binary number and assign powers of 2 to each digit (2⁰ on the right).
Multiply each digit by its corresponding power of 2.
Add the products to obtain the decimal value.

Examples

Example 1: convert 1011₂ to decimal

(1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (1 × 2^0)
= (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1)
= 8 + 0 + 2 + 1 = 11

Result: 1011₂ = 11₁₀.

Example 2: convert 11010₂ to decimal

(1 × 2^4) + (1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (0 × 2^0)
= 16 + 8 + 0 + 2 + 0 = 26

Result: 11010₂ = 26₁₀.

Binary to decimal conversion table

Quick reference values for short binary numbers.

References from binary (base 2) to decimal (base 10)
Binary	Decimal
`0`	0
`1`	1
`10`	2
`11`	3
`100`	4
`101`	5
`110`	6
`111`	7
`1000`	8
`1001`	9
`1010`	10
`10000`	16
`100000`	32
`1000000`	64
`10000000`	128
`100000000`	256
`1000000000`	512
`10000000000`	1024

Frequently Asked Questions

How do you convert a binary number to decimal?

To convert a binary number to decimal, multiply each binary digit by a power of 2 based on its position (starting from the right at 0) and then add up all the results. For example, binary 1011 is converted as: (1×2^3) + (0×2^2) + (1×2^1) + (1×2^0) = 11.

Why are powers of 2 used in the binary system?

The binary system only uses two digits: 0 and 1. Each position in a binary number represents a power of 2 (1, 2, 4, 8, 16, etc.), in the same way that each position in the decimal system represents a power of 10.

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