Writing a logic expression from a logic circuit: several gates

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Quick Questions

Shade in the A or B circle for each question.

1. A circuit has an AND gate (inputs A and B) whose output goes into an OR gate with input C. Which expression is correct?

A X = (A AND B) OR C

B X = A AND (B OR C)

2. When writing an expression for a multi-gate circuit, which gate's operator is the outermost one?

A The final gate, the one that gives output X

B The first gate on the left, next to the inputs

3. In which order do you build up the expression for a circuit?

A Right to left, starting with the gate that gives X

B Left to right, starting with the gates next to the inputs

4. A NOR gate (inputs A and B) feeds one input of an AND gate. The other AND input is C. Which expression is correct?

A X = (A AND B) NOR C

B X = (A NOR B) AND C

5. An OR gate (inputs A and B) feeds an AND gate along with input C. What is the correct expression?

A X = (A OR B) AND C

B X = A OR B AND C

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1X = (A AND B) OR C		AThe brackets are missing, so it is unclear which gate comes first. An AND gate feeding an OR gate with C should be written X = (A AND B) OR C.
2X = (A OR B) AND (B NOT C)		BAn AND gate takes A and B. Its output goes into an OR gate with C. The OR gate is the final gate that gives X.
3Each earlier gate's expression goes in brackets as an input to the next gate		CX = (A OR B) AND C
4The final gate in the circuit is the outermost operator in the expression		DNot valid
5X = A AND B OR C		Eplaceholder
6X = (A AND B) OR (C NOR A)		FX = NOT (A AND B) OR C

Definitions

X = (A AND B) OR C

Fill in the Blanks

Complete each line of code by filling in the missing parts.

X = (A AND B) __ C

P = A AND B X = _ OR C

X = (A OR B) AND ___ C

X = (A AND B) OR (B AND _)

P = A OR B Q = NOT C X = P ___ Q

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A AND(A,B) then OR with C

B P = A OR B

C X = P OR C

D X = (A AND B) OR C

Question 2

A P = A AND B

B Q = NOT C

C X = P AND Q

D X = (A OR B) AND (NOT C)

Question 3

A G1 = A AND B

B G2 = G1 OR C

C X = A AND B OR C

Question 4

A P = NOT B

B Q = P AND B

C X = (NOT A) AND B

D X = Q

Question 5

A Gate 1: B AND C gives P

B Gate 2: A OR P gives X

C X = (A OR B) AND C

Answer Key

Writing a logic expression from a logic circuit: several gates

Section A: Quick Questions

A — X = (A AND B) OR C

A — The final gate, the one that gives output X

B — Left to right, starting with the gates next to the inputs

B — X = (A NOR B) AND C

A — X = (A OR B) AND C

Section B: Match the Pairs

X = (A AND B) OR C → An AND gate takes A and B. Its output goes into an OR gate with C. The OR gate is the final gate that gives X.

X = (A OR B) AND (B NOT C) → Not valid

Each earlier gate's expression goes in brackets as an input to the next gate → X = (A OR B) AND C

The final gate in the circuit is the outermost operator in the expression → X = NOT (A AND B) OR C

X = A AND B OR C → The brackets are missing, so it is unclear which gate comes first. An AND gate feeding an OR gate with C should be written X = (A AND B) OR C.

X = (A AND B) OR (C NOR A) → placeholder

Section C: Definitions

X = (A AND B) OR C — Write each gate's expression from left to right, putting each earlier gate in brackets as an input to the next gate. The final gate is the outermost operator.

Section D: Fill in the Blanks

X = (A AND B) OR C

P = A AND B
X = P OR C

X = (A OR B) AND NOT C

X = (A AND B) OR (B AND C)

P = A OR B
Q = NOT C
X = P AND Q

Section E: Spot the Error

B — The first gate is an AND gate, so P = A AND B. Writing OR here makes the final expression (A AND B) OR C impossible.

A — The final expression uses (A OR B), so the first gate must be P = A OR B, not AND.

C — The first gate's expression must go in brackets as an input to the next gate. It should be X = (A AND B) OR C.

A — The NOT gate is on input A, so P = NOT A. The final expression (NOT A) AND B shows this.

C — The AND gate (B AND C) is the earlier gate, so it goes in brackets as an input to the final OR gate. It should be X = A OR (B AND C).