Free Binary/Decimal Converter

Electronic circuits have two reliable states: on and off. Binary (0 and 1) maps perfectly to this. More states would be harder to distinguish reliably and make circuits more complex.

Multiply each bit by 2 raised to its position (rightmost is position 0). Add all results. For 1101: 1×8 + 1×4 + 0×2 + 1×1 = 13.

For unsigned: 255 (11111111). For signed (two's complement): 127 (positive) to -128 (negative). The leading bit indicates sign in signed representation.

A way to represent negative numbers in binary. Flip all bits and add 1 to get the negative. For example, -1 in 8-bit two's complement is 11111111.

Binary addressing means memory and storage naturally come in powers of 2. 2^10=1024 (KB), 2^20=1048576 (MB), etc. This aligns with how binary counting works.

The 0x prefix indicates hexadecimal, not binary. Binary often uses 0b prefix (0b1101). However, both relate to binary since each hex digit equals 4 binary bits.