Tracing one input combination through a circuit

Name:

Date:

Class:

Quick Questions

Shade in the A or B circle for each question.

1. Where do you start when tracing one input combination through a circuit?

A Write the input values on the input wires on the left

B Write the final output X first, then work backwards

2. Which direction do you work when tracing a circuit?

A Right to left, from X back to the inputs

B Left to right, from the inputs towards X

3. A is 1 and B is 0 going into an AND gate. What do you write on the gate's output wire?

A 0

B 1

4. A is 1 and B is 0 going into an OR gate. What do you write on the gate's output wire?

A 0

B 1

5. A NOT gate has 1 on its input wire. What do you write on its output wire?

A 0

B 1

Match the Pairs

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

Left column		Right column
1A=1, B=0, A AND B = 0		AWrite 1 on wire A and 0 on wire B, then the AND gate outputs 0 on its output wire
2NOT gate: 0 in, 1 out		B(A OR B) AND C: do A OR B first, then AND with C
3Work through the gates from left to right, so a gate's inputs are known before you work out its output		CWrite the gate's output on its output wire so the next gate to the right can use it as an input
4The final answer is the value written on the last wire, which is the output X		DAND outputs 1 only when both inputs are 1. With inputs 1 and 0 the output on the wire should be 0, not 1.
5A=1, B=0: A AND B = 1		EA=1, B=1, C=0 gives X = (A AND B) OR C = 1
6Trace (A OR B) AND C: do AND first, then OR		FThe gates were traced in the wrong order. You must work left to right, so the OR gate is traced first and its output feeds the AND gate.

Definitions

trace a circuit

Fill in the Blanks

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

Trace a circuit from ____ to right

A = 1, B = 1 P = A NAND B = 1 NAND 1 = 0 X = NOT P = NOT 0 = _

A = 1, B = 0, C = 1 P = A AND B = 1 AND 0 = 0 X = P OR C = 0 OR 1 = _

A = 0, B = 1, P = A XOR B P = 0 ___ 1 = 1

The wire after the last gate is output _

Spot the Error

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

Question 1

A A=1 B=1 C=1

B P = A AND B = 1 AND 0 = 0

C X = P OR C = 0 OR 1 = 1

Question 2

A A=0 B=1 C=1

B P = NOT A = NOT 0 = 0

C Q = P AND B = 1 AND 1 = 1

D X = Q OR C = 1 OR 1 = 1

Question 3

A A=1 B=1

B P = A NAND B = 1 NAND 1 = 0

C Q = NOT B = NOT 1 = 0

D X = P OR Q = 0 OR 0 = 1

Question 4

A A=1 B=0 C=0

B P = A OR B = 1 OR 0 = 1

C Q = P AND C = 1 AND 0 = 0

D X = P = 1

Question 5

A A=0 B=1 C=0

B P = A XOR B = 0 XOR 1 = 1

C Q = P NOR C = 1 NOR 0 = 1

D X = Q = 0

Answer Key

Tracing one input combination through a circuit

Section A: Quick Questions

A — Write the input values on the input wires on the left

B — Left to right, from the inputs towards X

A — 0

B — 1

A — 0

Section B: Match the Pairs

A=1, B=0, A AND B = 0 → Write 1 on wire A and 0 on wire B, then the AND gate outputs 0 on its output wire

NOT gate: 0 in, 1 out → Write the gate's output on its output wire so the next gate to the right can use it as an input

Work through the gates from left to right, so a gate's inputs are known before you work out its output → (A OR B) AND C: do A OR B first, then AND with C

The final answer is the value written on the last wire, which is the output X → A=1, B=1, C=0 gives X = (A AND B) OR C = 1

A=1, B=0: A AND B = 1 → AND outputs 1 only when both inputs are 1. With inputs 1 and 0 the output on the wire should be 0, not 1.

Trace (A OR B) AND C: do AND first, then OR → The gates were traced in the wrong order. You must work left to right, so the OR gate is traced first and its output feeds the AND gate.

Section C: Definitions

trace a circuit — Write the input values on the wires, then work gate by gate from left to right, writing each gate's output on its output wire until you reach the final output X.

Section D: Fill in the Blanks

Trace a circuit from left to right

A = 1, B = 1
P = A NAND B = 1 NAND 1 = 0
X = NOT P = NOT 0 = 1

A = 1, B = 0, C = 1
P = A AND B = 1 AND 0 = 0
X = P OR C = 0 OR 1 = 1

A = 0, B = 1, P = A XOR B
P = 0 XOR 1 = 1

The wire after the last gate is output X

Section E: Spot the Error

A — The trace uses B as 0 in the AND gate (1 AND 0), so the inputs written on the wires must be A=1 B=0 C=1, not B=1.

B — A NOT gate flips its input. NOT 0 is 1, so the output wire P must be 1, not 0.

D — An OR gate outputs 1 only if at least one input is 1. With both inputs 0, the final output X is 0, not 1.

D — The final output X is the output of the last gate on the left-to-right path, which is Q. Q is 0, so the line should be X = Q = 0.

C — A NOR gate outputs 1 only when both inputs are 0. Here one input is 1, so the output is 0, not 1.