How to Convert Decimal to Binary (and Binary to Decimal) by Hand

The short answer

To convert a decimal number to binary, keep dividing by 2 and write down each remainder; the remainders read from bottom to top are the binary number. For example, 45 in binary is 101101. To go back, multiply each binary digit by its place value (1, 2, 4, 8, 16 and so on from the right) and add them up. You can check every answer with the Number Base Converter, which converts decimal to binary, octal and hexadecimal at once.

How binary place values work

In decimal, each position is worth 10 times the one to its right: ones, tens, hundreds. In binary, each position is worth 2 times the one to its right:

Position from the right	8th	7th	6th	5th	4th	3rd	2nd	1st
Place value	128	64	32	16	8	4	2	1

Each binary digit (bit) is either 0 or 1, meaning that place value is either left out or counted once. That single idea is enough for both directions of conversion.

Method 1: Decimal to binary by dividing by 2

Divide the number by 2.

Write down the remainder (it will always be 0 or 1).

Divide the whole-number result by 2 again, and write down the new remainder.

Repeat until the result is 0.

Read the remainders from the last one to the first one. That is the binary number.

Example: 45 to binary

Division	Result	Remainder
45 ÷ 2	22	1
22 ÷ 2	11	0
11 ÷ 2	5	1
5 ÷ 2	2	1
2 ÷ 2	1	0
1 ÷ 2	0	1

Reading the remainders from the bottom up gives 101101. So 45 in decimal is 101101 in binary.

Example: 156 to binary

156 ÷ 2 = 78 remainder 0, 78 ÷ 2 = 39 remainder 0, 39 ÷ 2 = 19 remainder 1, 19 ÷ 2 = 9 remainder 1, 9 ÷ 2 = 4 remainder 1, 4 ÷ 2 = 2 remainder 0, 2 ÷ 2 = 1 remainder 0, 1 ÷ 2 = 0 remainder 1.

Bottom to top: 10011100.

The most common mistake is reading the remainders from top to bottom, which would give 00111001 instead. If your answer starts with 0, you have almost certainly read it the wrong way round, because a binary number written without padding always starts with 1.

Method 2: Decimal to binary by subtracting place values

Some people find this faster for numbers under 256.

Find the largest place value that fits into your number (from 128, 64, 32, 16, 8, 4, 2, 1).

Put a 1 in that position and subtract the place value.

Move to the next smaller place value. If it fits into what is left, write 1 and subtract; otherwise write 0.

Continue down to the 1s place.

For 156: 128 fits (1, leaves 28), 64 does not (0), 32 does not (0), 16 fits (1, leaves 12), 8 fits (1, leaves 4), 4 fits (1, leaves 0), 2 does not (0), 1 does not (0). Result: 10011100, the same as Method 1.

Binary to decimal

Write the place values above the digits, starting with 1 on the right, and add the place values wherever there is a 1.

Example: 101101 to decimal

Place value	32	16	8	4	2	1
Binary digit	1	0	1	1	0	1

32 + 8 + 4 + 1 = 45.

Example: 11111111 to decimal

128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. This is the largest number that fits in 8 bits (one byte), which is why 255 appears so often in computing, for example as the maximum value of each colour channel in RGB.

Quick reference table

Decimal	Binary	Octal	Hexadecimal
13	1101	15	D
45	101101	55	2D
100	1100100	144	64
156	10011100	234	9C
255	11111111	377	FF
1024	10000000000	2000	400
2026	11111101010	3752	7EA

Every row was produced with the Number Base Converter.

Checking your answer with the converter

Open the Number Base Converter.

Type your whole number in the Value to convert box and choose Decimal (Base 10) in the From list.

The result box shows the unit picked in the To list (Binary by default), and the table underneath shows the same value in decimal, binary, octal and hexadecimal.

To check binary to decimal, choose Binary (Base 2) as the From unit and type the binary digits.

A few limits to keep in mind:

• The converter works with whole numbers. If you type 10.5 as a decimal, the fractional part is dropped and you get the binary for 10.
• For binary input, keep to 16 digits or fewer. Longer binary strings lose precision before conversion and can give a wrong result.
• Type decimal or binary values for input. Letters such as the A to F used in hexadecimal are not read correctly as input, so use decimal or binary as your starting value and read the hex result from the table.

Why the divide-by-2 method works

Each division by 2 asks: is this number even or odd? The remainder answers that for the current lowest bit. Dividing by 2 then shifts everything one place to the right, so the next remainder tells you the next bit. That is why the first remainder is the rightmost digit and you must read the list upwards.

The same method works for any base. To convert decimal to octal, divide by 8 and collect remainders (0 to 7). For hexadecimal, divide by 16 and write remainders 10 to 15 as A to F. For example, 156 ÷ 16 = 9 remainder 12, and 9 ÷ 16 = 0 remainder 9, so 156 is 9C in hex, matching the table.

Practice problems

Try these, then check them with the converter:

13 to binary (answer: 1101)

100 to binary (answer: 1100100)

10011100 to decimal (answer: 156)

2026 to binary (answer: 11111101010)

Related tools and guides

If you are converting text rather than numbers, letters are first turned into character codes and then into binary; see How to Convert Text to Binary (and Binary Back to Text) and the Binary Code Translator.