Boolean Algebra - Practice MCQs for CCAT

Correct Answer: C - A + B

Using absorption law: A + A'B = A + B.

Correct Answer: C - A

Idempotent law: A + A = A.

Correct Answer: B - 0

Complement law: A AND NOT A = 0.

Correct Answer: D - 1

Complement law: A OR NOT A = 1.

Correct Answer: A - A' + B'

De Morgan: NOT(A AND B) = NOT A OR NOT B.

Correct Answer: B - A' · B'

De Morgan: NOT(A OR B) = NOT A AND NOT B.

Correct Answer: B - A

A·B + A·B' = A(B + B') = A·1 = A.

Correct Answer: A - A

Identity law: A + 0 = A.

Correct Answer: D - A

Identity law: A · 1 = A.

Correct Answer: B - 1

Domination law: A + 1 = 1.

Correct Answer: C - 1

A + A' = 1. This is the complement law - a variable ORed with its complement always equals 1.

Correct Answer: D - Distributive Law

This is the distributive law of addition over multiplication in Boolean algebra.

Correct Answer: B - A

A + (A · B) = A. This is the absorption law - A absorbs the term (A · B).

Correct Answer: B - A + A = A

A + A = A is the idempotent law for OR. ORing a variable with itself gives the same variable.

Correct Answer: C - A

A · (A + B) = A. This is the absorption law - A absorbs the term (A + B).

Correct Answer: D - A product term with each variable appearing once

A minterm is a product (AND) term that contains each variable of the function exactly once, either in true or complemented form.

Correct Answer: B - A sum term with each variable appearing once

A maxterm is a sum (OR) term that contains each variable of the function exactly once, either in true or complemented form.

Correct Answer: C - B

A' · B + A · B = B · (A' + A) = B · 1 = B. Factor out B and apply complement law.

Correct Answer: A - A · (B + C)

The dual is obtained by swapping AND with OR and vice versa. Dual of A + B · C is A · (B + C).

Correct Answer: D - A · 1 = A

A · 1 = A is the identity law for AND. ANDing any variable with 1 gives the variable itself.

Correct Answer: A - A + 1 = 1

A + 1 = 1 is the null law for OR. ORing any variable with 1 always gives 1.

Correct Answer: A - OR of AND terms

SOP is a Boolean expression written as OR of AND terms (product terms), e.g., AB + CD + EF.

Correct Answer: B - AND of OR terms

POS is a Boolean expression written as AND of OR terms (sum terms), e.g., (A+B)(C+D)(E+F).

Correct Answer: A - Boolean expression simplification

Karnaugh maps provide a visual method to simplify Boolean expressions by grouping adjacent cells.

Correct Answer: D - One variable only

Adjacent cells in a K-map differ by exactly one variable, allowing simplification when grouped.

Correct Answer: C - A + B

Using the absorption theorem: A + A'B = A + B. This can be verified by expanding: A + A'B = A(1 + B) + A'B = A + AB + A'B = A + B(A + A') = A + B.

Correct Answer: B - Idempotent law

The Idempotent law states that A + A = A and A · A = A. ORing or ANDing a variable with itself yields the same variable.

Correct Answer: C - A · (B + C)

The dual of a Boolean expression is obtained by interchanging AND with OR and OR with AND, while keeping the variables unchanged. So the dual of A + BC is A · (B + C).

Correct Answer: D - A'B'

De Morgan's first theorem states: (A + B)' = A'B'. The complement of a sum equals the product of the complements.

Correct Answer: C - A

AB + AB' = A(B + B') = A · 1 = A. Factoring out A and applying the complement law B + B' = 1 gives the simplified result.

Correct Answer: B - 8

A K-map for n variables has 2ⁿ cells. For 3 variables: 2³ = 8 cells. The map is typically arranged as a 2×4 grid.

Correct Answer: D - 16

In a 4-variable K-map with 16 cells, the maximum group size is 16 (all cells), which simplifies to 1. Groups must be powers of 2: 1, 2, 4, 8, or 16.

Correct Answer: D - Absorption law

The absorption law states: A · (A + B) = A and A + AB = A. The variable A absorbs the second term.

Correct Answer: D - A'B + AB'

XOR gives output 1 when inputs differ. The minterms are: A=0,B=1 (A'B) and A=1,B=0 (AB'). So F = A'B + AB'.

Correct Answer: D - Horizontally, vertically adjacent and wrap-around edge cells

In a K-map, adjacency includes horizontal, vertical, and wrap-around edges (top-bottom and left-right). Diagonal cells are NOT considered adjacent.

Correct Answer: A - 1

Σm(0,1,2,3) includes all minterms for 2 variables (A'B', A'B, AB', AB). Since all combinations are covered, F = 1.

Correct Answer: D - AB + A'C

The consensus theorem states: AB + A'C + BC = AB + A'C. The term BC is redundant because it is covered by the other two terms (consensus term).

Correct Answer: A - 16

A function with n variables has 2ⁿ minterms. For 4 variables: 2⁴ = 16 minterms (m0 through m15).

Correct Answer: B - Invalid input combinations that can be treated as 0 or 1

Don't care conditions represent input combinations that either never occur or whose output doesn't matter. They can be treated as 0 or 1 during simplification to form larger groups.

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

POS form is a product (AND) of sum (OR) terms called maxterms. (A + B)(A + C) is a valid POS expression where each factor is a sum term.

Correct Answer: A - (A' + B')(C' + D')

Applying De Morgan's theorem: F' = (AB + CD)' = (AB)' · (CD)' = (A' + B')(C' + D'). The complement of a sum is product of complements, and complement of a product is sum of complements.

Correct Answer: C - 2

In K-map simplification, grouping 2^k cells eliminates k variables. A group of 4 = 2² cells eliminates 2 variables from the product term.

Correct Answer: C - 0

A ⊕ A = A'A + AA' = 0 + 0 = 0. XORing a variable with itself always gives 0.

Correct Answer: A - AB + A'B'

XNOR gives output 1 when both inputs are same. F = AB + A'B' (both 1s or both 0s). It is the complement of XOR.

Correct Answer: C - AB + BC + AC

Mapping minterms 3(011), 5(101), 6(110), 7(111) on K-map: m3 and m7 give BC, m5 and m7 give AC, m6 and m7 give AB. F = AB + BC + AC.

Correct Answer: A - F = xF(1) + x'F(0)

Shannon's expansion theorem: F(x) = x · F(x=1) + x' · F(x=0). This cofactor expansion is fundamental to many synthesis and verification algorithms.

Correct Answer: C - A product term that cannot be combined with any other term to form a simpler term

A prime implicant is a product term that cannot be further reduced by combining with other terms. It represents the largest possible grouping in a K-map.

Correct Answer: A - AB + AC

The distributive law states: A(B + C) = AB + AC. AND distributes over OR, similar to multiplication distributing over addition in regular algebra.

Correct Answer: B - 1

Minterms 1(001), 3(011), 5(101), 7(111) all have C=1. The only prime implicant is C, which covers all minterms. There is 1 essential prime implicant: C.

Correct Answer: A - A + B'

For 2 variables, maxterm M2 corresponds to the binary value 10 (A=1, B=0). The maxterm is formed by complementing: if variable is 1, take the variable as is; if 0, take the complement. So M2 = A + B' (note: in maxterms, 1→uncomplemented, 0→complemented in sum form, but the convention is M2 for (1,0) gives A' + B in some texts. The standard convention: Mi uses complement for 1 and true for 0 in POS: M2 = A' + B).