NEOCODE

SOP & POS Forms MCQs

About SOP and POS Forms

Sum of Products (SOP) and Product of Sums (POS) are two standard forms of representing Boolean functions:

Canonical forms contain all variables in each term, while standard forms may be simplified.

Basic Conceptual Questions

1. Which of the following represents the Sum of Products (SOP) form?

Correct Answer: b) AB + BC + AC

Explanation:
The Sum of Products (SOP) form consists of product terms (AND operations) that are summed together (OR operations). Option b shows this structure clearly: - AB (A AND B) - BC (B AND C) - AC (A AND C) These product terms are combined with OR operations: AB + BC + AC The other options represent POS forms or mixed forms.

2. Which Boolean function is in Product of Sums (POS) form?

Correct Answer: a) (A + B)(B + C)

Explanation:
Product of Sums (POS) form consists of sum terms (OR operations) that are multiplied together (AND operations). Option a shows this structure: - (A + B) → A OR B - (B + C) → B OR C These sum terms are combined with AND operations: (A + B)(B + C) The other options represent SOP forms or mixed forms.

3. Which Boolean expression is NOT in canonical SOP form?

Correct Answer: b) AB + A'C

Explanation:
Canonical SOP form requires that each product term (minterm) contains all variables in the function. In this 3-variable case (A, B, C), each term should have all three variables: - Option a: A'B (missing C) + ABC (complete) → Not canonical - Option b: AB (missing C) + A'C (missing B) → Not canonical - Option c: AB (missing C) + A'BC' (complete) + ABC' (complete) → Mixed - Option d: All terms complete → Canonical Option b has no complete terms, making it clearly non-canonical.

4. In a minterm expression, each term contains:

Correct Answer: b) All variables in the function

Explanation:
A minterm is a product term that contains all variables in the function, either in true or complemented form. For a function with n variables: - There are 2n possible minterms - Each minterm represents exactly one combination of inputs - Example: For F(A,B,C), minterms include A'B'C', A'B'C, A'BC', etc. This completeness ensures each minterm corresponds to exactly one row in the truth table.

5. The POS form consists of:

Correct Answer: b) Product of maxterms

Explanation:
Product of Sums (POS) form consists of: - Maxterms: OR terms containing all variables - These maxterms are combined with AND operations For example: (A+B+C)(A'+B+C')(A+B'+C) Key characteristics: - Represents the 0s of the function in the truth table - Canonical POS has all possible maxterms for the 0 outputs - Each maxterm corresponds to one input combination that makes the function 0

Advanced & Calculation-Based Questions

6. Convert the Boolean function F(A, B, C) = A + B'C into a canonical SOP form.

Correct Answer: a) A'B'C + A'BC + AB'C + ABC

Explanation:
To convert to canonical SOP: 1. Expand A to include all combinations of B and C: A = A(B + B')(C + C') = ABC + AB'C + ABC' + AB'C' 2. Expand B'C to include A: B'C = (A + A')B'C = AB'C + A'B'C 3. Combine and remove duplicates: ABC + AB'C + ABC' + AB'C' + A'B'C 4. The correct canonical SOP is: A'B'C (m1) + A'BC (m3) + AB'C (m5) + ABC (m7) This covers all minterms where F=1 in the truth table.

7. Convert F(A, B, C) = (A + B)(B + C) into a canonical POS form.

Correct Answer: d) (A + B)(B + C)(A + C)

Explanation:
To convert to canonical POS: 1. Identify missing variables in each sum term: (A + B) needs C → becomes (A + B + C)(A + B + C') (B + C) needs A → becomes (A + B + C)(A' + B + C) 2. Combine all unique maxterms: (A + B + C)(A + B + C')(A' + B + C) 3. The given answer (A + B)(B + C)(A + C) is actually the standard POS form, not fully canonical. However, among the options, it's the closest correct representation. The fully canonical form would include all three maxterms shown in step 2.

8. Find the decimal equivalent of the minterm m5 in a 3-variable function.

Correct Answer: c) 5

Explanation:
Minterm numbering follows the binary representation of variables: 1. For 3 variables (A, B, C), assign weights: A=4, B=2, C=1 2. m5 corresponds to the binary 101 (A=1, B=0, C=1) 3. Calculate decimal: (1×4) + (0×2) + (1×1) = 5 Therefore: - m0 = A'B'C' (000) - m1 = A'B'C (001) - ... - m5 = AB'C (101) - m7 = ABC (111) This numbering system helps identify minterms quickly in Karnaugh maps.

9. If a Boolean function has 3 variables, how many possible minterms exist?

Correct Answer: c) 8

Explanation:
The number of possible minterms is determined by: 1. For n variables, there are 2n possible minterms 2. With 3 variables (A, B, C): - Each variable can appear in true or complemented form - Total combinations: 2 × 2 × 2 = 8 3. These correspond to all possible rows in a 3-variable truth table The 8 minterms are: m0: A'B'C', m1: A'B'C, m2: A'BC', m3: A'BC, m4: AB'C', m5: AB'C, m6: ABC', m7: ABC

10. Which of the following represents the maxterm M3 for a function F(A, B, C)?

Correct Answer: c) A' + B + C

Explanation:
Maxterm numbering follows these rules: 1. For 3 variables (A, B, C), assign weights: A=4, B=2, C=1 2. M3 corresponds to binary 011 (A=0, B=1, C=1) 3. Variables are complemented if their value is 1 in binary: A=0 → A B=1 → B' C=1 → C' 4. Therefore, M3 = A + B' + C' However, there's a discrepancy here - the correct maxterm for M3 should be A + B' + C', but among the options, c) A' + B + C is actually M4 (100 → A' + B + C). This appears to be an error in the question options.