Quiz 2 — Boolean Algebra, Gates & Minterms/Maxterms

Question 1 of 15 · easy · Boolean Algebra Laws

Simplify: $A + AB$

Absorption law: $A + AB = A$.

Question 2 of 15 · easy · Logic Gates

The output of a NAND gate when both inputs are 1 is:

NAND(1,1) = NOT(AND(1,1)) = NOT(1) = 0.

Question 3 of 15 · easy · Boolean Algebra Laws

According to De Morgan's theorem, $\overline{A + B}$ equals:

De Morgan's: $\overline{A + B} = \overline{A} \cdot \overline{B}$. Break the bar, change OR to AND.

Question 4 of 15 · easy · Logic Gates

Which gates are called universal gates?

NAND and NOR are universal gates — any Boolean function can be implemented using only NAND or only NOR gates.

Question 5 of 15 · medium · Minterms

For 3 variables (A, B, C), the minterm $m_5$ is:

$5 = 101_2$ → A=1 (normal), B=0 (complemented), C=1 (normal) → $m_5 = A\overline{B}C$.

Question 6 of 15 · medium · Maxterms

For 3 variables (A, B, C), the maxterm $M_3$ is:

$3 = 011_2$ → A=0 → normal ($A$), B=1 → complemented ($\overline{B}$), C=1 → complemented ($\overline{C}$). $M_3 = A + \overline{B} + \overline{C}$.

Question 7 of 15 · medium · Conversion Between Forms

If $F(A,B,C) = \sum m(1, 3, 5, 7)$, the POS form is:

3 variables → indices {0-7}. Minterms {1,3,5,7} → Maxterms = complement = {0,2,4,6}. $F = \prod M(0,2,4,6)$.

Question 8 of 15 · medium · Boolean Algebra Laws

Simplify: $\overline{A} \cdot (\overline{A} + B)$

Absorption: $\overline{A}(\overline{A}+B) = \overline{A}$. (Since $X(X+Y) = X$).

Question 9 of 15 · easy · Logic Gates

$A \oplus B = A\overline{B} + \overline{A}B$

This is the definition of XOR. It outputs 1 when inputs are different.

Question 10 of 15 · easy · Minterms

How many minterms does a 4-variable Boolean function have?

$2^n = 2^4 = 16$ minterms for a 4-variable function.

Question 11 of 15 · easy · Boolean Algebra Laws

Simplify: $AB + A\overline{B}$

Factor: $A(B + \overline{B}) = A \cdot 1 = A$.

Question 12 of 15 · hard · Boolean Algebra Laws

In Boolean algebra, $A + BC = $?

Distributive law of OR over AND (unique to Boolean algebra): $A + BC = (A+B)(A+C)$.

Question 13 of 15 · easy · Maxterms

A maxterm $M_i$ equals 0 for exactly one input combination.

Each maxterm is defined to be 0 for exactly ONE input combination (the one corresponding to index $i$) and 1 for all others.

Question 14 of 15 · medium · Conversion Between Forms

What is the complement of $F = \sum m(0, 2, 5)$ for a 3-variable function?

The complement uses the remaining indices. All = {0,1,2,3,4,5,6,7}. F uses {0,2,5}. $\overline{F} = \sum m(1,3,4,6,7)$.

Question 15 of 15 · medium · Logic Gates

What is $1 \oplus 0 \oplus 1$?

Step by step: $1 \oplus 0 = 1$ (different → 1), then $1 \oplus 1 = 0$ (same → 0). Answer: 0.