Decimal to Binary Converter

Converting decimal to binary is the classic exercise of every intro programming and networking course, and a practical need when you work with bit flags, subnet masks or register values. This converter shows the repeated division by 2 that produces the bits, and can pad the result to a fixed width of 8, 16, 32 or 64 bits. With a width chosen, it also shows negative numbers the way computers store them: in two’s complement.

How to use the decimal to binary converter

1. Type the decimal number. Spaces and underscores are ignored, so 1_000_000 works.
2. Leave Convert from set to decimal. You can switch to binary, octal or hex at any time.
3. Optionally, pick a width under Pad the binary result to: 8, 16, 32 or 64 bits. The binary result is padded with leading zeros to that width.
4. For a negative number, choose a width to see it in two’s complement at that width.
5. Read the binary result, plus the octal and hex forms, and follow the division steps underneath. Use the copy button to copy any result.

How it works

Repeated division by 2

To turn a whole number into binary, divide it by 2 and keep the remainder, which is always 0 or 1. Divide the quotient by 2 again, and repeat until the quotient is 0. The remainders are the bits, from the lowest to the highest, so you read them from the bottom up.

Two’s complement for negative numbers

Most computers store signed integers in two’s complement at a fixed width. To get the pattern for −n:

1. Write n in binary at the chosen width.
2. Invert every bit (0 becomes 1, 1 becomes 0).
3. Add 1.

The result is the same as 2^width − n. MDN’s JavaScript reference uses the same representation: its bitwise NOT example shows −3 as thirty 1 bits followed by 01 in 32 bits, and it notes that BigInt values are encoded as two’s complement. The leftmost bit acts as the sign: 1 means negative.

A number has to fit in the width you choose. In 8 bits, signed values run from −128 to 127 and unsigned values from 0 to 255; in 16 bits, from −32,768 to 32,767 and 0 to 65,535.

Worked examples

13 → 1101

Division	Quotient	Remainder
13 ÷ 2	6	1
6 ÷ 2	3	0
3 ÷ 2	1	1
1 ÷ 2	0	1

Reading the remainders from the bottom up gives 1101. Check: 8 + 4 + 1 = 13. Padded to 8 bits it is 00001101.

156 → 10011100

Division	Quotient	Remainder
156 ÷ 2	78	0
78 ÷ 2	39	0
39 ÷ 2	19	1
19 ÷ 2	9	1
9 ÷ 2	4	1
4 ÷ 2	2	0
2 ÷ 2	1	0
1 ÷ 2	0	1

Bottom up: 10011100. Check: 128 + 16 + 8 + 4 = 156.

1000 → 1111101000

Ten divisions give the remainders 0, 0, 0, 1, 0, 1, 1, 1, 1, 1; read backward that’s 1111101000 (512 + 256 + 128 + 64 + 32 + 8 = 1,000). In hex it is 3E8.

−5 in 8 bits → 11111011

5 in 8 bits is 00000101. Invert every bit: 11111010. Add 1: 11111011. Check: 2⁸ − 5 = 251, and 11111011 is 251 read as unsigned. At 16 bits the same number is 1111111111111011.

−100 in 8 bits → 10011100

100 is 01100100; inverted, 10011011; plus 1, 10011100. That’s the same bit pattern as 156 above, because 256 − 100 = 156: whether those bits mean 156 or −100 depends on whether the program treats them as unsigned or signed.

Common values

Decimal	Binary	Padded to 8 bits
1	1	00000001
10	1010	00001010
127	1111111	01111111
255	11111111	11111111
−1	−1	11111111 (two’s complement)
−128	−10000000	10000000 (two’s complement)

Note that 255 and −1 share the same 8-bit pattern: as with 156 and −100, only the signed or unsigned reading tells them apart.

Related guides

• Going the other way? Use the binary to decimal converter, which adds up the powers of 2.
• Need hex instead? The hex to decimal converter shows the place values of base 16.
• Linux file permissions are three groups of three bits written in octal: the chmod calculator turns them into 755-style modes.