Subtraction of binary numbers is simple.

Rules for subtraction of binary numbers are similar to the rules for subtraction of decimal numbers.

The subtraction table of binary numbers:

10 - 1 = 1

1 - 0 = 1

1 - 1 = 0

0 - 0 = 0

1 - 0 = 1

1 - 1 = 0

0 - 0 = 0

Here, all numbers are binary.

Example

An example in the binary numeral system:

10 - 1 = 1

We convert left and right side of this equation to the decimal numeral system:

1 * 2^{1} + 0 * 2^{0} - 1 * 2^{0} = 1 * 2^{0}

and we get in the decimal numeral system:

2 + 0 - 1 = 1

Example

Subtract 10 from 100:

100

- 10

10

- 10

10

Here, we first subtract the zero of the subtrahend from the right zero of the 100, and after, we took 1 of position 3 to subtract 1 from the middle zero to the 100. Just as in the decimal system, but there are only 0 and 1 and the subtraction table at our disposal.

Example

One more example of subtraction of two binary numbers:. Subtract 10 from 1001:

1001

- 10

111

- 10

111

Example

The last example of subtracting two binary numbers. Subtract 1 from 1000:

1000

- 1

111

- 1

111

For more detailed information see Binary subtraction rules.