EEE 120 Final Test Questions and Correct
Answers
AND gate truth table
Output is 1 ONLY when ALL inputs are 1. (0,0→0; 0,1→0; 1,0→0; 1,1→1)
OR gate truth table
Output is 1 when AT LEAST ONE input is 1. (0,0→0; 0,1→1; 1,0→1; 1,1→1)
NOT gate (Inverter) truth table
Output is the complement of the input. (0→1; 1→0)
NAND gate truth table
Output is 0 ONLY when ALL inputs are 1. (0,0→1; 0,1→1; 1,0→1; 1,1→0) — complement
of AND
NOR gate truth table
Output is 1 ONLY when ALL inputs are 0. (0,0→1; 0,1→0; 1,0→0; 1,1→0) — complement
of OR
XOR gate truth table
Output is 1 when inputs are DIFFERENT. (0,0→0; 0,1→1; 1,0→1; 1,1→0) — Y = A'B +
AB'
XNOR gate
Output is 1 when inputs are the SAME. Complement of XOR. (0,0→1; 0,1→0; 1,0→0;
1,1→1)
NAND gate — alternate symbol (DeMorgan)
,OR gate with INVERTED (bubbled) inputs. Equivalent to (AB)'
NOR gate — alternate symbol (DeMorgan)
AND gate with INVERTED (bubbled) inputs. Equivalent to (A+B)'
Bubble on a gate input
Represents inversion (NOT) at that input. A bubble on the output also inverts the output.
Universal gate
A gate that can implement any Boolean function by itself. NAND and NOR are both
universal gates.
DeMorgan's Law #1
(A · B)' = A' + B' — The complement of an AND is the OR of the complements
DeMorgan's Law #2
(A + B)' = A' · B' — The complement of an OR is the AND of the complements
How to apply DeMorgan's Law
Break the bar, change the operator (AND↔OR). Complement each literal.
NAND expressed via DeMorgan
(AB)' = A' + B'
NOR expressed via DeMorgan
(A+B)' = A' · B'
Idempotency rule
A · A = A and A + A = A — combining identical inputs eliminates one gate
, OR with 1 rule
A + 1 = 1 — any OR with a constant 1 produces 1
AND with 0 rule
A · 0 = 0 — any AND with a constant 0 produces 0
Complement rule
A · A' = 0 and A + A' = 1
Double complement rule
(A')' = A
Minterm
A product (AND) term in which every variable appears exactly once (complemented or
uncomplemented). Row where output = 1.
Maxterm
A sum (OR) term in which every variable appears exactly once. Row where output = 0.
Sum of Minterms (shorthand)
Σm(#, #, ...) — lists the row numbers where the output is 1
Product of Maxterms (shorthand)
ΠM(#, #, ...) — lists the row numbers where the output is 0
Sum of Products (SOP) form
Boolean expression written as OR of AND terms (minterms). Example: Y = AB' + A'B + AB
Product of Sums (POS) form
Answers
AND gate truth table
Output is 1 ONLY when ALL inputs are 1. (0,0→0; 0,1→0; 1,0→0; 1,1→1)
OR gate truth table
Output is 1 when AT LEAST ONE input is 1. (0,0→0; 0,1→1; 1,0→1; 1,1→1)
NOT gate (Inverter) truth table
Output is the complement of the input. (0→1; 1→0)
NAND gate truth table
Output is 0 ONLY when ALL inputs are 1. (0,0→1; 0,1→1; 1,0→1; 1,1→0) — complement
of AND
NOR gate truth table
Output is 1 ONLY when ALL inputs are 0. (0,0→1; 0,1→0; 1,0→0; 1,1→0) — complement
of OR
XOR gate truth table
Output is 1 when inputs are DIFFERENT. (0,0→0; 0,1→1; 1,0→1; 1,1→0) — Y = A'B +
AB'
XNOR gate
Output is 1 when inputs are the SAME. Complement of XOR. (0,0→1; 0,1→0; 1,0→0;
1,1→1)
NAND gate — alternate symbol (DeMorgan)
,OR gate with INVERTED (bubbled) inputs. Equivalent to (AB)'
NOR gate — alternate symbol (DeMorgan)
AND gate with INVERTED (bubbled) inputs. Equivalent to (A+B)'
Bubble on a gate input
Represents inversion (NOT) at that input. A bubble on the output also inverts the output.
Universal gate
A gate that can implement any Boolean function by itself. NAND and NOR are both
universal gates.
DeMorgan's Law #1
(A · B)' = A' + B' — The complement of an AND is the OR of the complements
DeMorgan's Law #2
(A + B)' = A' · B' — The complement of an OR is the AND of the complements
How to apply DeMorgan's Law
Break the bar, change the operator (AND↔OR). Complement each literal.
NAND expressed via DeMorgan
(AB)' = A' + B'
NOR expressed via DeMorgan
(A+B)' = A' · B'
Idempotency rule
A · A = A and A + A = A — combining identical inputs eliminates one gate
, OR with 1 rule
A + 1 = 1 — any OR with a constant 1 produces 1
AND with 0 rule
A · 0 = 0 — any AND with a constant 0 produces 0
Complement rule
A · A' = 0 and A + A' = 1
Double complement rule
(A')' = A
Minterm
A product (AND) term in which every variable appears exactly once (complemented or
uncomplemented). Row where output = 1.
Maxterm
A sum (OR) term in which every variable appears exactly once. Row where output = 0.
Sum of Minterms (shorthand)
Σm(#, #, ...) — lists the row numbers where the output is 1
Product of Maxterms (shorthand)
ΠM(#, #, ...) — lists the row numbers where the output is 0
Sum of Products (SOP) form
Boolean expression written as OR of AND terms (minterms). Example: Y = AB' + A'B + AB
Product of Sums (POS) form
