Representing a signed number with 1's complement is done by changing
all the bits that are 1 to 0 and all the bits that are 0 to 1. Reversing
the digits in this way is also called complementing a number. Let's
look at an example in 4-bit arithmetic. How can we represent the number
-510 in 1's complement?
- First, we write the positive value of the number in binary.
- Next, we reverse each bit of the number so 1's become 0's
and 0's become 1's
To the right is a table of 4-bit binary numbers in 1's complement notation.
Notice that all of the negative values begin with a 1. Whenever we use
1's complement notation, the most significant bit always tells us the
sign of the number. The only exception to this rule is -0. In 1's complement,
we have two ways of representing the number zero. Notice also that the
values +0 to +7 are the same as the normal binary representation. Only
the negative values must be complemented. You should verify for yourself
that these negative values are correct by using the steps below to produce
Here is a quick summary of how to find the 1's complement representation
of any decimal number x.
- If x is positive, simply convert x to binary.
- If x is negative, write the positive value of x in
- Reverse each bit.