Thursday, February 25, 2016

1's and 2's Complement

1's and 2's Complement, Example: 1’s complement and 2’s complement are two important binary concepts. Two’s complement is especially important because it allows us to represent signed numbers in binary, and one’s complement is the interim step to finding the two’s complement.
  • 1’s Complement
If all bits in a byte are inverted by changing each 1 to 0 and each 0 to 1, we have formed the one’s complement of the number.
 
Original       One's Complement
-------------------------------
10011001  -->  01100110
10000001  -->  01111110
11110000  -->  00001111
11111111  -->  00000000
00000000  -->  11111111
  
  • 2’s Complement
The two’s complement is a method for representing positive and negative integer values in binary. The useful part of two’s complement is that it automatically includes the sign bit.

Step 1: Begin with the original binary value

    10011001  Original byte

Step 2: Find the one's complement

    01100110  One's complement

Step 3: Add 1  to the one's complement

    01100110  One's complement
  +        1  Add 1
 -----------
    01100111  <---  Two's complement

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