Intermediate columns in a truth table

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Intermediate columns in a truth table

Name:
Date:
Class:
A

Quick Questions

Shade in the A or B circle for each question.

1. For X = (A AND B) OR C, which extra column would you fill in first?
A P = A AND B
B P = A OR C
2. Why add an intermediate column to a truth table?
A To work out one gate or bracket at a time
B To add an extra input to the circuit
3. For X = (NOT A) AND B, a column Q holds NOT A. What is Q when A = 1?
A Q = 0
B Q = 1
4. Which column is filled in last for X = (A AND B) OR C?
A The intermediate column P
B The final output column X
5. In the row A = 1, B = 1, what is P if P = A AND B?
A P = 0
B P = 1
B

Match the Pairs

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

Left columnRight column
1P = A AND B AX = Q AND P
2Q = NOT A BThe intermediate column P should be completed first. X uses P, so filling in X before P makes the step by step method impossible and invites errors.
3Work out the bracket first in its own column P, then use P with C to find the final output X CP = A AND B, X = P OR C
4Give the NOT A result its own column Q, then combine Q with the P column in the last column DAn intermediate column that holds the opposite of input A in each row, ready to be used in a later column
5Row A=1, B=0: P = A AND B = 1 EAn intermediate column that holds the output of the bracket (A AND B) for every row, before the final output X is worked out
6Final column X = (A AND B) OR C, filled in before column P FP is worked out wrongly. 1 AND 0 gives 0, because AND needs both inputs to be 1. The wrong value in P then spoils the final output X.
C

Definitions

intermediate column
D

Fill in the Blanks

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

1.
X = (A AND B) OR C P = A ___ B
2.
X = (NOT A) AND B Q = ___ A
3.
X = (A AND B) OR (NOT A) P = A AND B, Q = NOT A X = P __ Q
4.
X = (A AND B) OR C _ = A AND B X = P OR C
5.
P = A AND B Q = NOT A X = _ OR Q
E

Spot the Error

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

Question 1
A X = (A AND B) OR NOT A
B P = A OR B
C Q = NOT A
D X = P OR Q
Question 2
A X = (A OR B) OR NOT C
B P = A OR B
C Q = NOT C
D X = P AND Q
Question 3
A X = NOT A AND (B OR C)
B P = NOT A
C Q = B OR C
D X = P OR Q
Question 4
A A = 1, B = 0
B P = A AND B = 0
C Q = NOT A = 1
D X = P OR Q = 0
Question 5
A X = (NOT A) OR B
B P = NOT B
C X = P OR B

Answer Key

Intermediate columns in a truth table
Section A: Quick Questions
Q1
A — P = A AND B
Q2
A — To work out one gate or bracket at a time
Q3
A — Q = 0
Q4
B — The final output column X
Q5
B — P = 1
Section B: Match the Pairs
Q1
P = A AND B → An intermediate column that holds the output of the bracket (A AND B) for every row, before the final output X is worked out
Q2
Q = NOT A → An intermediate column that holds the opposite of input A in each row, ready to be used in a later column
Q3
Work out the bracket first in its own column P, then use P with C to find the final output X → P = A AND B, X = P OR C
Q4
Give the NOT A result its own column Q, then combine Q with the P column in the last column → X = Q AND P
Q5
Row A=1, B=0: P = A AND B = 1 → P is worked out wrongly. 1 AND 0 gives 0, because AND needs both inputs to be 1. The wrong value in P then spoils the final output X.
Q6
Final column X = (A AND B) OR C, filled in before column P → The intermediate column P should be completed first. X uses P, so filling in X before P makes the step by step method impossible and invites errors.
Section C: Definitions
Q1
intermediate column — An extra truth table column for a bracket or gate output, such as P = A AND B. It is filled in first, so the final output X can be worked out step by step from earlier columns.
Section D: Fill in the Blanks
Q1
X = (A AND B) OR C P = A AND B
Q2
X = (NOT A) AND B Q = NOT A
Q3
X = (A AND B) OR (NOT A) P = A AND B, Q = NOT A X = P OR Q
Q4
X = (A AND B) OR C P = A AND B X = P OR C
Q5
P = A AND B Q = NOT A X = P OR Q
Section E: Spot the Error
Q1
B — The bracket in the expression is (A AND B), so intermediate column P must be A AND B, not A OR B.
Q2
A — The expression must match the columns below it. Columns P and Q are combined with AND, so the expression should be X = (A OR B) AND NOT C.
Q3
D — The expression joins NOT A and (B OR C) with AND, so the final column must be X = P AND Q.
Q4
C — When A is 1, NOT A is 0, so the value in column Q is 0. The line should be Q = NOT A = 0.
Q5
B — Column P holds the first part of the expression, which is NOT A. It should be P = NOT A, not NOT B.