CUET PG 2021 — Computer PYQ
CUET PG | Computer | 2021In the expression A + BC, the total numbers of minterms will be
Choose the correct answer:
- A.
2
- B.
3
- C.
4
- D.
5
(Correct Answer)
5
Explanation
Step 1: Expand Term A
To make A a minterm, we multiply it by (B+Bˉ) and (C+Cˉ):
A=A(B+Bˉ)(C+Cˉ)
A=A(BC+BCˉ+BˉC+BˉCˉ)
A=ABC+ABCˉ+ABˉC+ABˉCˉ
These correspond to minterms: {m7,m6,m5,m4}.
Step 2: Expand Term BC
To make BC a minterm, we multiply it by (A+Aˉ):
BC=BC(A+Aˉ)
BC=ABC+AˉBC
These correspond to minterms: {m7,m3}.
Step 3: Combine and Remove Duplicates
Now, we combine all the terms found above:
F=(ABC+ABCˉ+ABˉC+ABˉCˉ)+(ABC+AˉBC)
Removing the duplicate term (ABC):
F=ABC+ABCˉ+ABˉC+ABˉCˉ+AˉBC
The set of unique minterms is:
Minterms={m7,m6,m5,m4,m3}
Final Solution
Counting the unique terms in the expression:
Total number of minterms=5
Explanation
Step 1: Expand Term A
To make A a minterm, we multiply it by (B+Bˉ) and (C+Cˉ):
A=A(B+Bˉ)(C+Cˉ)
A=A(BC+BCˉ+BˉC+BˉCˉ)
A=ABC+ABCˉ+ABˉC+ABˉCˉ
These correspond to minterms: {m7,m6,m5,m4}.
Step 2: Expand Term BC
To make BC a minterm, we multiply it by (A+Aˉ):
BC=BC(A+Aˉ)
BC=ABC+AˉBC
These correspond to minterms: {m7,m3}.
Step 3: Combine and Remove Duplicates
Now, we combine all the terms found above:
F=(ABC+ABCˉ+ABˉC+ABˉCˉ)+(ABC+AˉBC)
Removing the duplicate term (ABC):
F=ABC+ABCˉ+ABˉC+ABˉCˉ+AˉBC
The set of unique minterms is:
Minterms={m7,m6,m5,m4,m3}
Final Solution
Counting the unique terms in the expression:
Total number of minterms=5