A Boolean variable takes which values?
A Any integer
B Only positive values
C Zero or one
D A continuous range
Answer: C. Zero or one. Boolean algebra uses binary values representing false and true.
A sum-of-products expression combines product terms using what?
A OR operation
B AND operation only
C XOR operation only
D Clock pulses
Answer: A. OR operation. SOP expressions OR together terms formed by AND operations.
A product-of-sums expression combines sum terms using what?
A OR operation only
B AND operation
C NOT operation only
D Clock pulses
Answer: B. AND operation. POS expressions AND together terms formed by OR operations.
A minterm contains every variable in what form?
A Only complemented variables
B Exactly once
C No variables
D At least twice
Answer: B. Exactly once. A minterm includes each input variable in true or complemented form.
A maxterm is a sum term that evaluates to zero for what?
A Every input combination
B No input combination
C One input combination
D Two combinations only
Answer: C. One input combination. A maxterm is zero for one unique input row.
Adjacent K-map cells differ in how many variables?
A Two variables
B All variables
C One variable
D No variables
Answer: C. One variable. K-map adjacency represents a change in one input bit.
K-map groups should contain how many cells?
A Prime numbers only
B Odd counts only
C Any number
D Power of two
Answer: D. Power of two. Groups of 1, 2, 4, 8 and so on enable Boolean simplification.
A don’t-care condition may be assigned what value?
A Only zero
B Only one
C Zero or one
D Neither value
Answer: C. Zero or one. Don’t-care terms can be chosen to simplify a logic function.
An implicant is a product term covering what?
A Only maxterms
B Clock edges
C State registers
D One or more minterms
Answer: D. One or more minterms. An implicant covers minterms for which the function is one.
A prime implicant cannot be combined into what larger term?
A A maxterm
B A clock signal
C Another implicant
D A register
Answer: C. Another implicant. A prime implicant is not contained in a larger valid implicant.
An essential prime implicant covers a minterm covered by what?
A Every minterm
B Only a don’t-care
C A maxterm only
D No other prime implicant
Answer: D. No other prime implicant. An essential prime implicant uniquely covers at least one required minterm.
The principle of duality swaps AND with OR and zero with what?
A One
B XOR
C NOT
D Clock
Answer: A. One. Boolean duality interchanges AND/OR and 0/1.
Which Boolean law states A + AB = A?
A De Morgan law
B Absorption law
C Associative law
D Commutative law
Answer: B. Absorption law. Absorption removes a redundant product term.
NAND and NOR gates are called what?
A Universal gates
B Sequential gates
C Analog gates
D Storage gates
Answer: A. Universal gates. Either NAND or NOR gates can implement any Boolean function.
XNOR outputs one when inputs are what?
A Equal
B Different
C Both zero only
D Both one only
Answer: A. Equal. XNOR is the complement of XOR and is true for matching inputs.
An active-low signal is asserted when it is what?
A Logic zero
B Logic one
C High impedance
D Clock edge
Answer: A. Logic zero. Active-low signals use a low voltage level to indicate assertion.
A bubble on a logic symbol usually indicates what?
A Clock input
B Power supply
C Inversion
D High impedance
Answer: C. Inversion. A bubble denotes logical inversion at an input or output.
De Morgan’s theorem transforms a complemented OR into what?
A OR of complements
B AND of complements
C XOR of inputs
D NOR of clocks
Answer: B. AND of complements. NOT(A OR B) equals NOT A AND NOT B.
The consensus theorem can eliminate what term?
A Required minterm
B Clock input
C State bit
D Redundant product term
Answer: D. Redundant product term. The consensus theorem identifies terms implied by other product terms.
Propagation delay is time from input change to what?
A Clock start
B Power-up only
C Reset release only
D Output response
Answer: D. Output response. Propagation delay measures circuit response time after an input transition.
Logic depth is the number of gate levels along what?
A Input pins
B Longest signal path
C Power rails
D K-map cells only
Answer: B. Longest signal path. Logic depth estimates the number of cascaded gate stages.
Fan-in is the number of what for a gate?
A Outputs
B Power rails
C Clock cycles
D Inputs
Answer: D. Inputs. Fan-in counts input terminals on a logic gate.
Fan-out is the number of gate inputs driven by what?
A One output
B One clock cycle
C One state bit only
D One K-map group
Answer: A. One output. Fan-out measures the load an output can drive.
A static hazard causes a brief output glitch during what?
A Steady input state
B Input transition
C Power-off
D Memory refresh only
Answer: B. Input transition. Unequal path delays can produce a temporary glitch even when the ideal output stays constant.
Gray-code-adjacent values differ in how many bits?
A One bit
B Two bits
C All bits
D No bits
Answer: A. One bit. Gray code changes only one bit between adjacent values.