Page 15 - DCAP104_EXPOSURE_TO_COMPUTER_DISCPLINES
P. 15
Exposure to Computer Disciplines
Notes Arithmetic Addition: The complexity of arithmetic addition is dependent on the representation,
which have been followed. Let us discuss this with the help of following example.
Add 25 and - 30 in binary using 7 bit register in
Solution signed magnitude representation.
signed 1’s complement
signed 2’s complement.
Solution: 25 or +25 is
0 01 1001
- 30 in signed magnitude representation is:
+30 is 0 01 1 1 lo,
therefore - 30 is 1 01 11 I0
To do the arithmetic addition with one negative number we have to check tlie magnitude of the
numbers. The number having smaller magnitude is then subtracted from tlie bigger number
and the sign of bigger number is selected. The implementation of such a scheme in digital
hardware will require a long sequence of control decisions as well as circuits that will add,
compare and subtract numbers. Is there a better alternative than this scheme? Let us first try
the signed 2’s complement.
–30 in signed 2’s complement notation will be:
+30 is 0011110
–30 is 1100010 (2’ complement of 30 including sign bit)
+25 is 0011001
–25 is 1100111
Addition
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