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๐Ÿ”ข Binary to Decimal Converter

Convert binary numbers to decimal, hex, octal, and more โ€” with interactive bit-toggle input, live positional breakdown, signed integer support, and batch mode.

Binary Input
Integer type:
Interactive Bit Toggle (click to flip)
Batch Converter
Quick Values
Powers of 2
2โฟ Decimal Hex
How It Works
Formula:
d = ฮฃ bแตข ร— 2โฑ
Example: 1011
1ร—2ยณ + 0ร—2ยฒ + 1ร—2ยน + 1ร—2โฐ
= 8 + 0 + 2 + 1
= 11
Two's complement:
MSB has weight โˆ’2โฟโปยน instead of +2โฟโปยน
Number Bases
BinaryBase 2 ยท digits 0,1
OctalBase 8 ยท digits 0โ€“7
DecimalBase 10 ยท digits 0โ€“9
HexBase 16 ยท 0โ€“9 + Aโ€“F

About Binary to Decimal Conversion

Positional Notation

Binary uses base-2 positional notation. Each bit position represents a successive power of 2, starting from 2โฐ = 1 on the right. To convert to decimal, multiply each bit (0 or 1) by its positional value and sum the results.

Signed Integers

Two's complement is the standard way computers represent negative numbers. The most significant bit (MSB) has a negative weight (โˆ’2โฟโปยน). For example, 11111111 in 8-bit two's complement = โˆ’128 + 64+โ€ฆ+1 = โˆ’1 rather than 255.

Hexadecimal Shortcut

Every group of 4 binary digits maps directly to a single hex digit (0โ€“F). This makes hex a convenient shorthand for binary: 0000=0, 0001=1, โ€ฆ 1010=A, 1011=B, 1100=C, 1101=D, 1110=E, 1111=F.

Overflow & Ranges

An n-bit unsigned integer can hold values 0 to 2โฟโˆ’1. An n-bit signed (two's complement) integer holds โˆ’2โฟโปยน to 2โฟโปยนโˆ’1. Common sizes: 8-bit (0โ€“255 / โˆ’128 to 127), 16-bit (0โ€“65535 / โˆ’32768 to 32767), 32-bit, 64-bit.