Basic Electrical and Electronics Engineering: Unit IV: Digital Electronics
Complements
with Solved Example Problems
Complements are used in digital computers for simplifying the subtraction operation and for logical manipulation.
COMPLEMENTS
Complements
are used in digital computers for simplifying the subtraction operation and for
logical manipulation. There are two types of complements for each base 'r'
system. The two methods are
(i) r's complement
(ii) (r-1)'s complement
For
binary number, r = 2 and r-1 = 1, so the 1's complement of N is (2n
- 1) - N. For r's complement of an n-digit number N in base r is defined as rn
- N for N ≠ 0 and 0 for N = 0.
1's complement
The
1's complement of a binary number is obtained by change all 1's to zero and
zeros to ones.
Problem: 35
Find I's complement of (10110)2
Solution:
(101
10)2 → 0 1 0 0 1
Problem: 36
Find I's complement of (110111)2
Solution:
(1
10 1 1 1)2 → (001 000)
2's complement:
The
2's complement is obtained by adding one to the 1's complement of the given
number.
2's
complement = 1's complement +1
Problem: 37
Find 2's complement of (10011)2
Solution:
1's complement
1's
complement = 01100
2's complement
2's
complement = 01101
Problem: 38
Find 2's complement of (110110)2
Solution:
1's complement
2's complement
(110110)2 → 2's complement =
(001010)
Basic Electrical and Electronics Engineering: Unit IV: Digital Electronics : Tag: : with Solved Example Problems - Complements
Basic Electrical and Electronics Engineering: Unit IV: Digital Electronics
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