Page 16 - DCAP104_EXPOSURE_TO_COMPUTER_DISCPLINES

Unit 1: Data Information

Please note how easy is to add two numbers using signed 2’s Complement. This procedure requires Notes
only one control decision in one circuit for adding the two numbers. But it put additional condition
that the negative numbers should be stored in signed 2’s complement form in the registers. This
can be achieved by complementing the positive number bit by bit and then incrementing the
resultant by 1 to get signed 2’s complement.

Signed 1’s Complement Representation: Another possibility, which also is simple, is use of
signed 1’s complement. Signed 1’s complement has a rule. Add the two numbers, including the
sign bit. If carry of the most significant bit or sign bit is one, then increment the result by 1 and
discard the carry over. Let us repeat all the operations with
1’s complement.

Since, the carry out is 1, so add I to sum and discard the carry
1 000 111

1
1 001 000
+55 is 0 110 111

–55 is 1’s complement 1 001 000
Another interesting feature about these representations is the representation of 0. In signed
magnitude and 1’s complement there are two representations for zero as:

Signed magnitude + 0 -0
0 000000 1 000000
Signed 1’s complement 0 000000 1 111111
But in signed 2’s complement there is just one zero and there is no positive or negative zero.

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