Boolean Algebra

What Boolean Algebra covers

Boolean Algebra is examined on component 01 of OCR Computer Science, Computer systems. 85 recall questions across 5 subtopics.

The 5 subtopics

Each one has its own page.

• Logic Gates and Truth TablesRecall questions on truth tables, the AND, OR, NOT, XOR, NAND and NOR gates with their symbols and tables, reading and drawing gate diagrams, writing expressions from circuits, and proving equivalence with a truth table.Open →
• Defining Problems Using Boolean LogicRecall questions on turning English conditions into Boolean expressions, deriving sum-of-products expressions from truth tables, at least one, exactly one and all, majority voting, common mistakes, and checking an expression against its requirement.Open →
• Boolean Algebra Rules and SimplificationRecall questions on the notations and symbols for AND, OR, NOT, equivalence and exclusive OR, the commutative, associative and distributive laws, double negation, De Morgan's laws, basic identities, simplifying expressions and checking a simplification with a truth table.Open →
• Karnaugh MapsRecall questions on Karnaugh maps for two, three and four variables, Gray code labelling, filling a map, grouping rules, reading terms from groups, wrapping edges and corners, worked simplifications, and the advantages and limits of the method.Open →
• Half Adders, Full Adders and D-type Flip FlopsRecall questions on half adders and full adders with their truth tables, expressions and gate arrangements, ripple carry adders and propagation delay, tracing a four-bit addition, and D-type flip flops, edge triggering, toggling and their uses.Open →

What you need to know

Answer each one before you reveal it.

Take Boolean Algebra further

The same content, four other ways.

Commonly confused

Pairs that lose marks when they are blurred together.

• A half adder vs A full adder

  A half adder: a circuit adding two bits and producing a sum and a carry out. A full adder: a circuit adding two bits together with a carry in, so several can be chained.

• A Karnaugh map vs A truth table

  A Karnaugh map: a grid arrangement used to simplify an expression by grouping adjacent terms. A truth table: a table listing every combination of inputs and the output each produces.

• A ripple carry adder vs A D-type flip flop

  A ripple carry adder: several one-bit circuits chained so each carry feeds the next. A D-type flip flop: a circuit that stores one bit, taking its input only on a clock edge.

Questions from this topic

Each one with the model answer underneath.

1. 1

   What is a truth table, and how many rows does one need?

   Model answer

   A table listing every possible combination of the input values to a logic circuit or expression, with the resulting output for each. Because each input is either 0 or 1, a circuit with n inputs needs 2 to the power n rows: 4 rows for two inputs, 8 for three, 16 for four. The input columns are normally written in ascending binary order so that no combination is missed.

2. 2

   Describe the AND gate: its symbol, its behaviour and how the operation is written.

   Model answer

   The symbol is a shape with a flat left edge and a semicircular right edge, like a capital D, with the inputs entering on the left and the single output leaving from the curved right side. The output is 1 only when every input is 1, and 0 otherwise. Common ways of writing it are A.B, AB, A AND B and A and B joined by a wedge; several notations are accepted, so use whichever you are comfortable with as long as it is unambiguous.

3. 3

   Give the truth table for a two-input AND gate.

   Model answer

   With inputs A and B: 0 and 0 give 0; 0 and 1 give 0; 1 and 0 give 0; 1 and 1 give 1. Only the last row produces a 1.

4. 4

   Describe the OR gate and give its truth table.

   Model answer

   The symbol is a shield or arrowhead shape: a curved left edge that the inputs pass through, with the two upper and lower edges sweeping to a point on the right where the output leaves. The output is 1 when at least one input is 1. Truth table: 0,0 gives 0; 0,1 gives 1; 1,0 gives 1; 1,1 gives 1. It is usually written A+B, A OR B, or with a vee between the terms.

5. 5

   Describe the NOT gate and give its truth table.

   Model answer

   The symbol is a small triangle pointing right with a circle (a bubble) on its tip, with one input on the left and one output on the right. It inverts its single input: an input of 0 gives an output of 1, and an input of 1 gives an output of 0. It may be written as A with a bar over it, as A', or as a not-sign in front of A - all are accepted.

6. 6

   Describe the XOR gate and give its truth table.

   Model answer

   The symbol is the OR shape with an additional curved line drawn just outside and parallel to its curved left edge. Exclusive OR gives an output of 1 when the inputs are different and 0 when they are the same. Truth table: 0,0 gives 0; 0,1 gives 1; 1,0 gives 1; 1,1 gives 0. It is written with a plus sign inside a circle, or as A XOR B.

What is inside Levo

Six ways to work the same material.

Boolean Algebra revision questions

What does Boolean Algebra cover in OCR A-Level Computer Science?

5 subtopics: logic gates and truth tables, defining problems using boolean logic, boolean algebra rules and simplification, karnaugh maps and half adders, full adders and d-type flip flops. Each one has its own page with questions and model answers.

How is Boolean Algebra organised?

By the OCR H446 specification, subtopic by subtopic, so it matches the order you are taught it in.