1’s compliment:
case 1:
1001 1001
-1000 => 0111(complimented)
__________ __________
10000
=> 1
-----------
0001
why?
--> a-b = a + (1111-b) – 1111
if a +
(1111-b) > 1111 ans is posetive.
when a
+ (1111-b) > 1111 then a + (1111-b) have to be bigger than three bit.
So, a-b = a + (1111-b) -1111
= a + (1111-b) – 1000 + 1.
case 2:
when a + (1111-b) < 1111
1000 1000
-1001 => 0110(complimented)
__________ __________
1110 =>
-0001(complimented)
So, a-b = a + (1111-b) -1111
= - (1111 –
(a + (1111-b))
).
2’s
compliment:
case 1:
1001 0111(complimented)
-1000 => +
1
__________ __________
1000
=> 1001
-----------
10001 => 0001
a-b = a
+ (1111-b + 1) -10000.
case 2:
1000 0110 (complimented)
-1001 => +1
__________ __________
0111
+1000
----------
1111 => 0000(complm.)
+ 1 = 0001
=> - 0001
why ? a
- b = a + (1111 - b + 1) -10000 = - ( (1111 – (a + (1111 - b + 1) ) ) + 1 )
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