Boolean Logic

What is the output of NOT TRUE?

What is the output of TRUE AND FALSE?

What is the output of FALSE OR TRUE?

Complete the truth table for A AND B: A=0,B=0: ? A=0,B=1: ? A=1,B=0: ? A=1,B=1: ?

Draw (or describe) the logic gate symbol for OR and state its function.

What does a NOT gate do?

Complete the truth table for A OR B: A=0,B=0: ? A=0,B=1: ? A=1,B=0: ? A=1,B=1: ?

Construct a complete truth table for a NOT gate, showing both possible inputs and their outputs.

Which logic gate produces an output of 1 only when ALL of its inputs are 1?

A 3-input AND gate has inputs A, B and C. For how many of the 8 possible input combinations is the output 1?

What is an XOR gate and how is it different from OR?

A NAND gate produces a LOW output only when all its inputs are HIGH. Using a truth table, confirm the output of a 2-input NAND gate for all input combinations.

What is the function of an XOR (exclusive OR) gate and how does it differ from a standard OR gate?

Construct a truth table for a 2-input NOR gate, showing the output for all four input combinations.

For a 2-input XOR gate, what is the output when A=1 and B=1?

A 2-input NAND gate has inputs A=1 and B=0. What is its output?

A 2-input NOR gate has inputs A=0 and B=0. What is its output?

Explain how the truth table for a NAND gate relates to the truth table for an AND gate.

Which row of a 2-input XOR truth table produces an output of 0?

A 2-input NAND gate has inputs A=1 and B=1. What is its output, and how does this differ from a standard AND gate with the same inputs?

Simplify the Boolean expression: A AND TRUE

Simplify the Boolean expression: A OR FALSE

Simplify the Boolean expression: A AND FALSE

Simplify the Boolean expression: A OR A

Simplify the Boolean expression: A AND A

Simplify the Boolean expression: NOT(NOT A)

Simplify the Boolean expression: A OR (A AND B)

Simplify the Boolean expression: A AND (A OR B)

Use Boolean algebra to simplify: (A AND B) OR (A AND NOT B)

Explain why simplifying a Boolean expression before building a logic circuit is useful in practice.

Draw (or describe) a logic circuit for the Boolean expression: A AND B AND C

Draw (or describe) a logic circuit for the Boolean expression: (A OR B) AND C

Which combination of logic gates would correctly implement the expression NOT(A AND B)?

Draw (or describe) a logic circuit for the Boolean expression: A AND (NOT B)

How many logic gates, and of what types, are needed to draw a circuit for the expression (A OR B) AND (C OR D)?

Draw (or describe) a logic circuit for the expression: NOT A OR B

A circuit consists of an XOR gate and an AND gate, both taking inputs A and B, with their outputs feeding into a final OR gate. Which Boolean expression does this circuit represent?

Draw (or describe) the logic circuit for a half adder, which outputs Sum = A XOR B and Carry = A AND B.

A circuit for the expression A OR (B AND C) requires which gates, connected how?

Draw (or describe) a logic circuit for the expression: (A AND B) OR (NOT A AND C)

Evaluate: (A OR B) AND (NOT C) when A=1, B=0, C=0

A half adder circuit takes two 1-bit binary inputs. What are its two outputs and what are their values when both inputs are 1?

Construct a truth table for the expression: (A OR B) AND (NOT A)

Evaluate the expression NOT(A OR B) when A=1 and B=0.

Evaluate the expression (A AND B) OR C when A=0, B=1, C=1.

Evaluate the expression (A XOR B) AND C when A=1, B=1, C=1.

Evaluate the expression NOT A AND NOT B when A=0 and B=0.

A circuit computes the expression (A OR B) AND (C OR D). Evaluate its output for A=0, B=0, C=1, D=0.

A logic circuit takes inputs A, B and C and produces the output of A AND (B OR C). Trace through the circuit to find the output when A=1, B=0, C=0.

A circuit computes (A NAND B) OR C. Evaluate its output for A=1, B=1, C=0.

De Morgan's first law states that NOT(A OR B) is equivalent to which expression?

State De Morgan's second law.

Apply De Morgan's law to simplify: NOT(A AND B AND C)

Use De Morgan's law to simplify: NOT(NOT A OR NOT B)

Which pair of standard gates is equivalent to a NOR gate, as shown by De Morgan's law (NOT(A OR B) = NOT A AND NOT B)?

Apply De Morgan's law to rewrite NOT(A OR B) AND C without any negation of a bracketed OR expression.

Why are De Morgan's laws useful when designing logic circuits using only NAND gates (a "NAND-only" design)?

Use a truth table to verify that NOT(A AND B) produces the same outputs as (NOT A) OR (NOT B) for all input combinations.

Apply De Morgan's law to simplify: NOT(NOT A AND NOT B)

A student simplifies NOT(A AND B) to "NOT A AND NOT B" — a common mistake. Explain the error and state the correct simplification using De Morgan's law.