Completing a truth table from a logic circuit

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Completing a truth table from a logic circuit

Name:
Date:
Class:
A

Quick Questions

Shade in the A or B circle for each question.

1. Which describes the correct way to complete a truth table from a logic circuit?
A Trace each row of inputs through the gates one at a time and record the output
B Guess the output of X from the shape of the circuit and fill in the column
2. A circuit has three inputs A, B and C. How many rows does its truth table need?
A 6 rows
B 8 rows
3. A circuit is X = (A AND B) OR C. What is the best use of an extra column?
A Add a column for A AND B and write that gate's output in it
B Add a column that repeats the value of C for every row
4. A circuit has an AND gate with A = 1 and B = 0 feeding an OR gate with C = 0. What is X?
A 0
B 1
5. Where does the final value for the X column come from?
A The output of the first gate in the circuit, copied into the table
B The output of the last gate in the circuit, copied into the table
B

Match the Pairs

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

Left columnRight column
1X = (A AND B) OR C AA B | D = A AND B | X = NOT D
2A=1, B=0, C=1: A AND B = 0, so X = 0 OR 1 = 1 BA circuit with two gates: A and B go into an AND gate, and its output goes into an OR gate with C to give X. Work out the AND column first, then X.
3A three-input circuit needs a truth table with eight rows, covering every combination of A, B and C. CA B C: 000, 001, 010, 011, 100, 101, 110, 111
4Label each gate's output with its own column, so the value that leaves one gate and goes into the next is recorded. DThe NOT gate was applied wrongly. NOT 1 is 0, not 1, so X should be 0 on this row.
5A=1, B=1: A AND B = 1, so X = NOT 1 = 1 ETracing one row of a three-input truth table: write the AND gate output first, then use it to find X.
6Truth table for a three-input circuit with only four rows FThree inputs need eight rows. With only four rows, half of the input combinations were never traced through the circuit.
C

Definitions

trace each row
D

Fill in the Blanks

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

1.
P = A AND B X = NOT _
2.
A = 1, B = 0, C = 1 P = A AND B P = _
3.
Inputs: A, B, C Rows: 2 x 2 x 2 = _
4.
P = 1 X = NOT P X = _
5.
P = 1, X = 0 X = ___ P
E

Spot the Error

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

Question 1
A X = (A OR B) OR C
B P = A AND B
C Row A=1 B=1 C=0: P = 1
D X = P OR C = 1
Question 2
A Columns: A, B, X
B P = A OR B
C X = NOT P
Question 3
A Row: A=1, B=1
B P = A AND B = 0
C X = NOT P = 0
Question 4
A Row: A=0, B=1, C=1
B P = A OR B = 1
C Q = P AND C = 1
D X = NOT Q = 1
Question 5
A X = A NOR B
B Row: A=0, B=1
C A NOR B = 1, so X = 1
D Copy 0 into the X column

Answer Key

Completing a truth table from a logic circuit
Section A: Quick Questions
Q1
A — Trace each row of inputs through the gates one at a time and record the output
Q2
B — 8 rows
Q3
A — Add a column for A AND B and write that gate's output in it
Q4
A — 0
Q5
B — The output of the last gate in the circuit, copied into the table
Section B: Match the Pairs
Q1
X = (A AND B) OR C → A circuit with two gates: A and B go into an AND gate, and its output goes into an OR gate with C to give X. Work out the AND column first, then X.
Q2
A=1, B=0, C=1: A AND B = 0, so X = 0 OR 1 = 1 → Tracing one row of a three-input truth table: write the AND gate output first, then use it to find X.
Q3
A three-input circuit needs a truth table with eight rows, covering every combination of A, B and C. → A B C: 000, 001, 010, 011, 100, 101, 110, 111
Q4
Label each gate's output with its own column, so the value that leaves one gate and goes into the next is recorded. → A B | D = A AND B | X = NOT D
Q5
A=1, B=1: A AND B = 1, so X = NOT 1 = 1 → The NOT gate was applied wrongly. NOT 1 is 0, not 1, so X should be 0 on this row.
Q6
Truth table for a three-input circuit with only four rows → Three inputs need eight rows. With only four rows, half of the input combinations were never traced through the circuit.
Section C: Definitions
Q1
trace each row — Follow one row of input values through each gate in the circuit, write each gate's output in an extra column, then copy the final value of X into the truth table.
Section D: Fill in the Blanks
Q1
P = A AND B X = NOT P
Q2
A = 1, B = 0, C = 1 P = A AND B P = 0
Q3
Inputs: A, B, C Rows: 2 x 2 x 2 = 8
Q4
P = 1 X = NOT P X = 0
Q5
P = 1, X = 0 X = NOT P
Section E: Spot the Error
Q1
A — The circuit has an AND gate feeding the OR gate, so the expression must be X = (A AND B) OR C. Line 1 uses OR, which does not match the intermediate column P = A AND B.
Q2
A — The gate in the middle needs its own column. The table should have an extra column P (A, B, P, X) so the output of the OR gate can be written down before the NOT gate.
Q3
B — An AND gate outputs 1 only when both inputs are 1. With A=1 and B=1, P = 1, not 0.
Q4
D — A NOT gate reverses its input. Q is 1, so X = NOT Q = 0, not 1.
Q5
C — A NOR gate outputs 1 only when both inputs are 0. Here B is 1, so the output is 0 and X = 0.