Logic Expressions
1. Understanding the Syntax
In IGCSE, expressions can be written in two ways. You must be comfortable with both:
- Textual: $X = (\text{A AND B}) \text{ OR (NOT C)}$
- Symbolic: $X = (A \cdot B) + \bar{C}$
2. Worked Example: Building a Truth Table
Scenario: Create a truth table for the expression:
X = (A AND B) OR (NOT C)
Step-by-Step Breakdown
1 Identify Inputs: There are 3 inputs (A, B, C). This means there are $2^3 = 8$ possible combinations.
2 Create Intermediate Columns: Solve the brackets first. Create a column for
(A AND B) and another for (NOT C).
3 Final Output: Use the
OR gate to combine the two intermediate columns.
The Resulting Truth Table
| A | B | C | A AND B | NOT C | X |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 | 1 |
3. Common Logic Gates Combinations
- NAND Logic: $\text{NOT (A AND B)}$ is the same as saying "Output 0 only when A and B are 1".
- NOR Logic: $\text{NOT (A OR B)}$ is the same as saying "Output 1 only when A and B are both 0".
⚠️ Exam Tip: Always use Intermediate Columns. Even if the question doesn't ask for them, drawing them on your scrap paper prevents simple logic errors that ruin the entire final output column.