Boolean Logic · 5 question types
Past paper frequency (2018 to 2024)
This topic accounts for approximately 6% of your exam marks.
Writing Boolean expressions from logic diagrams and simplifying using laws appear regularly.
When the question gives you a truth table and asks for the Boolean expression, the standard method is called sum-of-products (also called SoP, or "minterm form"). The idea: write one AND term ("product") per row where the output is 1, then OR all those AND terms together (the "sum").
Sum-of-products method. (1) Find every row where
Q = 1. (2) For each such row, write an AND term that is true on that row only: use the variable directly when its value in that row is1, and¬variablewhen its value is0. (3) OR all the AND terms together.
Example — consider this truth table for a three-input circuit:
| A | B | C | Q |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |
Step 1: find the Q = 1 rows: row 5 (A = 1, B = 0, C = 0) and row 8 (A = 1, B = 1, C = 1).
Step 2: write one AND term per row:
A · ¬B · ¬C (use A directly because A=1; use ¬B because B=0; use ¬C because C=0). This AND term is 1 only when A=1, B=0, C=0.A · B · C (all three are 1, so use each variable directly). This AND term is 1 only when A=1, B=1, C=1.Step 3: OR them together:
Q = (A · ¬B · ¬C) + (A · B · C)
This expression is 1 on exactly the rows where the truth table says Q = 1, and 0 on every other row.
The brackets around each AND term are not strictly needed (AND binds tighter than OR anyway), but they make the structure clearer and are usually included in mark-scheme answers.
An AND term that is
1on exactly one row of the truth table is called a minterm. The sum-of-products expression is the OR of all the minterms for theQ = 1rows.