Decimal to binary converter

Divide the number by 2, write down the remainder (0 or 1), and divide the quotient again. Stop when the quotient is 0. The binary number is the remainders read bottom up.

Bottom up: 10011100. The first remainder is the last bit, because it says whether the number is even. The same method works for any base: divide by 16 for hex, by 8 for octal.

Find the largest power of two that fits, subtract it, and repeat with what is left. Each power you used is a 1 bit.

156 - 128 = 28   → 128s place: 1
 28 -  64          →  64s place: 0 (too big)
 28 -  32          →  32s place: 0 (too big)
 28 -  16 = 12     →  16s place: 1
 12 -   8 =  4     →   8s place: 1
  4 -   4 =  0     →   4s place: 1
                       2s place: 0, 1s place: 0
156 = 1001 1100

A binary number has no leading zeros, but stored values have a fixed width. 156 is 10011100 as a byte, 00000000 10011100 as a 16-bit value. Pick the width in the converter and it pads, and warns you if the number does not fit.

Fixed-width signed integers use two’s complement. To write -x in N bits:

-20 in 8 bits
 20       = 0001 0100
 invert   = 1110 1011
 add 1    = 1110 1100   ← -20

Check: as unsigned, 1110 1100 is 236, and 236 - 256 = -20. Python’s bin(-20) prints -0b10100 with a minus sign instead, because Python integers have no fixed width; mask it to get the bits: format(-20 & 0xFF, '08b').

For the part after the point, multiply by 2. The whole part of each result (0 or 1) is the next bit; keep the fraction and repeat.

0.625 × 2 = 1.25  → 1
0.25  × 2 = 0.5   → 0
0.5   × 2 = 1.0   → 1      0.625 = 0.101

0.1 × 2 = 0.2 → 0
0.2 × 2 = 0.4 → 0
0.4 × 2 = 0.8 → 0
0.8 × 2 = 1.6 → 1
0.6 × 2 = 1.2 → 1
0.2 × 2 = 0.4 → 0  ← 0.2 again: it repeats
0.1 = 0.0(0011)

The converter finds where a fraction starts repeating and shows the repeating digits in brackets, so you get the exact answer instead of a rounded one.

// JavaScript
(156).toString(2)                     // '10011100'
(10).toString(2).padStart(8, '0')     // '00001010'
BigInt.asUintN(8, -20n).toString(2)   // '11101100' (two's complement)

# Python
bin(156)              # '0b10011100'
format(10, '08b')     # '00001010'
f'{156:b}'            # '10011100'

// Go
strconv.FormatInt(156, 2)       // "10011100"
fmt.Sprintf("%08b", 10)         // "00001010"

# Bash
echo "obase=2; 156" | bc        # 10011100

The reverse is on the binary to decimal page, and the binary converter handles hex, octal and any base up to 36.

Every byte value in decimal, 8-bit binary and hex.