Decimal to Binary Converter

Going the other way? Convert binary back to decimal →

How do you convert decimal to binary?

Decimal to binary conversion divides the number by 2 over and over, keeping each remainder, then reads the remainders from the last one back to the first.

1. Divide the number by 2 and write down the remainder. 156 ÷ 2 leaves 0.
2. Divide the quotient by 2 again and keep that remainder too.
3. Repeat until the quotient reaches 0.
4. Read the remainders from bottom to top: 156 = 10011100.

Decimal to Binary Conversion Table

Every position in a binary number is worth twice the one to its right. Binary writes values on the digit set 0, 1, each place worth 2ⁿ, and a value marked with the 0b prefix is binary. A byte is 8 bits and holds 256 values, 0–255; a nibble is 4 bits. Add the weights under the 1s and you have the decimal value; divide by 2 and keep remainders to go the other way.

Each base is defined by three things: which digits it uses, how a value is marked, and what each position is worth.

Worked Example: 156 to Binary

One value, converted the long way so the working is visible. This is the same grid the converter shows when you turn on "show steps".

Divide by 2 and keep the remainder, then divide the quotient again, until the quotient reaches 0. For 156 that runs: 156 / 2 = 78 remainder 0; 78 / 2 = 39 remainder 0; 39 / 2 = 19 remainder 1; 19 / 2 = 9 remainder 1, and on down to 0.

The remainders come out least significant first, so they are read from the bottom of the list back to the top: 10011100. Reading them the other way is the single most common error, and it gives a number that looks plausible and is wrong. The check is quick — expand the result back and it must return 156.

Check it in reverse

The value returns unchanged. Convert 10011100 back and you get 156, because a base change rewrites the digits without touching the quantity they stand for. That is the whole test: if the round trip differs, a digit was misread. To check it by hand, check the value by converting binary back to decimal and compare it with the number you started from.

Worked examples: decimal to binary

Each example gives the value first, then the working. Click a value to load it in the converter.

Every example above reverses exactly — read the same bits back as decimal.

What About Padding, Fractions and Width?

Leading zeros and width

A number carries no leading zeros unless a width is fixed. 10011100 and 010011100 are the same value, so the converter writes the short form. Fixed widths belong to bytes and registers, not to arithmetic. how to write a negative number in binary covers where width does matter.

Fractions and the point

Digits after a point convert by the same rule with negative powers, so the first place after the point is worth 1/2. Many fractions that end neatly in decimal repeat forever in binary, which is where rounding creeps in.

Negative values

A minus sign is kept in front of the digits. Fixed-width binary encodes sign differently, using two's complement, and that is a separate rule from the base change itself.

How large a value can be

The method has no ceiling; each extra decimal digit multiplies the range by 10. Practical limits come from the width a machine stores the value in, not from the conversion.

Decimal to Binary in Code

The same rule in one line. Both divide repeatedly and return the digits in order.

Python: format(156, 'b')

JavaScript: (156).toString(2)

Common Mistakes

• Reading the remainders top to bottom. They come out in reverse, so the digits land backwards.
• Using a digit the base does not have — an 8 in octal, or a 2 in binary. The value cannot be read at all.
• Grouping bits from the left. Groups are counted from the right, and the leftmost group is the one that gets padded.
• Treating the result as a character code. 65 is a number here, not the letter A.

Frequently Asked Questions

Related Conversions

• Decimal also converts to hex by the same route — write a number in base 16.
• Decimal also converts to octal by the same route — how to change decimal to octal by dividing by 8.
• Decimal also converts to text by the same route — decimal code values to ASCII characters.
• If your input is text rather than decimal, turn words into binary code instead.
• If your input is hex rather than decimal, expand each hex digit to four bits instead.
• If your input is hex rather than decimal, hex to dec by 16^n weights instead.

The rest of the family sits on the whole binary and text converter set.