Mathematics

Binary Decimal Calculator

Number Base Converter

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Enter Decimal Number

What is Binary Decimal Calculator?

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A binary to decimal (and decimal to binary) converter translates between base 2 and base 10. Binary is the native language of digital computers; decimal is the human number system.

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Formula

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f(x)Binary to decimal: Σ (bit value × 2^position); Decimal to binary: repeatedly divide by 2, read remainders in reverse

Variable Legend

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Symbol	Name	Unit	Description
b	Binary digit (0 or 1)	—	—
d	Decimal value	—	—
n	Bit position (rightmost = 0)	—	—

How to Binary Decimal Calculator

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1Binary to decimal: each bit position = 2ⁿ, sum the 1-positions
2Decimal to binary: divide by 2 repeatedly, read remainders in reverse
38-bit byte: values 0–255; 16-bit: 0–65,535
4Signed integers use two's complement for negative numbers

Worked Examples

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Example 1

Given:Binary 11001010

Result:128+64+0+0+8+0+2+0 = 202 decimal

Real-World Applications

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Understanding computer memory

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Low-level programming and assembly

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Networking and IP addressing

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Digital signal processing

Powers of 2

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Bit position	2ⁿ value
0	1
1	2
2	4
3	8
4	16
7	128
8	256
15	32,768

Frequently Asked Questions

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Why do computers use binary?

Binary matches the on/off states of transistors in circuits. 1 = on/high voltage, 0 = off/low voltage.

What is a byte?

A byte is 8 bits. It can represent values from 0 (00000000) to 255 (11111111).

How are negative numbers represented?

Two's complement: flip all bits and add 1. Example: −5 as 8-bit = 11111011.

References

›Binary number system — Khan Academy

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Reviewed October 2026

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