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?

  1. First, we write the positive value of the number in binary.
 0101 (+5)
  1. Next, we reverse each bit of the number so 1's become 0's and 0's become 1's
 1010 (-5)



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 this table.

Binary

0111
0110
0101
0100
0011
0010
0001
0000
1111
1110
1101
1100
1011
1010
1001
1000

Decimal

+7
+6
+5
+4
+3
+2
+1
+0
-0
-1
-2
-3
-4
-5
-6
-7


Here is a quick summary of how to find the 1's complement representation of any decimal number x.

  1. If x is positive, simply convert x to binary.
  2. If x is negative, write the positive value of x in binary
  3. Reverse each bit.