This section deepens four skills from computing systems and logic: building nested truth tables, checking equivalence, turning words into conditions, and separating how many bits a value uses from the value itself.
All four rely on one habit: check every input combination, and never trust a result you tested on only one case.
What are the four skills?
| Order | Skill | The mark it protects |
|---|---|---|
| 1 | Building a truth table from a nested expression | Correct columns and order of evaluation |
| 2 | Checking a claimed equivalence | Proving or disproving with all rows |
| 3 | Converting a written requirement into a condition | Choosing AND or OR and the right brackets |
| 4 | Distinguishing size from value | Bits needed versus number stored |
Test them together in the integrated practice set.
One sentence, two tables
An original requirement: “A member gets a discount if they are under 12 or over 60 and they have a card.”
Read as (under 12 OR over 60) AND card, a child without a card gets nothing. Read as under 12 OR (over 60 AND card), a child without a card gets the discount.
The words are the same but the truth tables differ. Skills 1 and 3 show how to build the table and how to remove the ambiguity with brackets.
Who should start where?
If your tables have wrong columns, begin with skill 1. If you are asked whether two expressions are equal and guess, begin with skill 2. If a word problem gives you an expression you cannot defend, begin with skill 3.
Skill 4 stands on its own. Begin there if questions about bytes or bits give you a different answer each time. Use the Boolean expression and truth-table explorer to check any table.
What next?
Go through the four lessons in order. To go through your own tables with a teacher, see online one-to-one Computer Science tuition.