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Answer the following Boolean algebra questions: . Find its corresponding Cardinal and Canonical…
Answer the following Boolean algebra questions:
(a)[3.0]
$f(a, b, c) = a.b' + a.c + b.c'$. Find its corresponding Cardinal and Canonical sum-of-product expression?
(b)[2.0]
If $a=1, b=0, c=1, d=0$, then write maxterm and minterm for $F(a, b, c, d)$ in canonical form?
Answer
Answer (a)
AI$f(a,b,c) = a.b' + a.c + b.c'$
Truth table:
Cardinal (sum-of-minterms) form: $f(a,b,c) = \Sigma(2,4,5,6,7)$
Canonical SOP: $f(a,b,c) = a'bc' + ab'c' + ab'c + abc' + abc$
| a | b | c | f |
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
Answer (b)
AI$a=1, b=0, c=1, d=0$ gives the binary code 1010, i.e. index 10.
Minterm (variable uncomplemented if its value is 1, complemented if 0): $m_{10} = a.b'.c.d'$
Maxterm (variable complemented if its value is 1, uncomplemented if 0): $M_{10} = a' + b + c' + d$
From ISC Computer Science - Competency Focused Practice Questions (CISCE, August 2024), question 69.
Check your working with the Boolean algebra solver: the steps law by law, the K-map and the logic circuit for any expression.