(a) The logic circuit below has two inputs (A and B) and one output (X). Complete the truth table for this circuit. A B NOT A X 0 0 0 1 1 0 1 1 [4] (b) Writ...
Question 1 Report
(a) The logic circuit below has two inputs (A and B) and one output (X).
Complete the truth table for this circuit.
| A | B | NOT A | X |
|---|---|---|---|
| 0 | 0 | ||
| 0 | 1 | ||
| 1 | 0 | ||
| 1 | 1 |
[4]
(b) Write the Boolean expression for output X.
[2]
(c) Describe in words a real-world situation that this logic circuit could model.
[2]
(d) Draw a truth table for the Boolean expression X = A OR (NOT B).
[3]
(e) State two uses of logic gates in everyday electronic devices.
[2]
Answer Details
(a) The circuit passes input A through a NOT gate, then feeds the result (NOT A) and input B into an AND gate to produce output X. The truth table is completed by evaluating each row:
| A | B | NOT A | X = (NOT A) AND B |
|---|---|---|---|
| 0 | 0 | 1 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 |
Row 1: NOT 0 = 1; 1 AND 0 = 0. [1]
Row 2: NOT 0 = 1; 1 AND 1 = 1. [1]
Row 3: NOT 1 = 0; 0 AND 0 = 0. [1]
Row 4: NOT 1 = 0; 0 AND 1 = 0. [1]
(b) X = (NOT A) AND B [1+1]
This reads: the output X is 1 only when A is 0 (NOT A = 1) and B is 1.
(c) A real-world example: a security light that turns on (X = 1) when it is dark outside (A = 0, meaning NOT A = 1) AND motion is detected (B = 1). During daytime (A = 1) or when there is no motion (B = 0), the light stays off. [2]
(d) Truth table for X = A OR (NOT B):
| A | B | NOT B | X = A OR (NOT B) |
|---|---|---|---|
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
Row 1: NOT 0 = 1; 0 OR 1 = 1. [1]
Row 2: NOT 1 = 0; 0 OR 0 = 0. [1]
Row 3: NOT 0 = 1; 1 OR 1 = 1.
Row 4: NOT 1 = 0; 1 OR 0 = 1. [1]
(e) Two uses of logic gates in everyday electronic devices:
- Burglar alarm systems use logic gates to combine signals from multiple sensors (door, window, motion) and determine whether to trigger the alarm. [1]
- Calculator circuits use combinations of logic gates to perform arithmetic and logical operations on binary numbers. [1]
Download The App On Google Playstore
Everything you need to excel in your exams
