ZAK's Boolean Algebra & K-map Lab
Every part of the Paper 3 logic question in one place. Type an expression, click a truth table or fill a K-map and get the sum-of-products, the optimal loops drawn the way Cambridge draws them, the simplified sum-of-products, the simplest form and the Boolean algebra working with each law named. Then Practice — random questions in the exact shape of the 2021–2026 papers, marked like the mark scheme — and the live adders and flip-flops. Theory in Hardware and Virtual Machines.
Past-paper example library
35 real questions from 9618 Paper 3 (2021–2026) with the mark-scheme answer — every shape the examiners use. Press Past-paper examples to search them.
Truth table → K-map 8
Given the truth table: write the sum-of-products, complete the K-map, draw loops, simplify
Expression → K-map 8
Given a sum-of-products: complete the K-map, loop it, write the simplified sum-of-products and simplest form
De Morgan's laws 6
Simplify using De Morgan's laws and Boolean algebra, showing every stage
Boolean algebra 5
Simplify with the laws — absorption, redundancy, distributive, complement, identity
Circuit → truth table 4
Complete the truth table for a logic circuit, with the working columns P, Q, R, S
Half & full adders 2
Name the circuit, complete its truth table, state the purpose of each output
Flip-flops 2
SR and JK flip-flops — draw, derive the truth table, explain the invalid state
How the exam question goes — and how this lab follows it
- Circuit → truth table [3]. One mark for the working columns (P, Q, R, S — one per gate), one for each half of the output column. The Solve tab draws any expression as a circuit and labels the gates; Practice → Circuit gives you the diagram and marks your table.
- Truth table → sum-of-products [2–3]. One product per row where the output is 1, every variable in every product, no simplification. Marked one mark per two correct products.
- Complete the K-map [2]. AB along the top and CD down the side (A down the side, BC along the top for three inputs), in the order 00 01 11 10. Every cell needs a 0 or a 1; one error costs one mark, two cost both.
- Draw loops for an optimal sum-of-products [1 per loop]. Groups of 1, 2, 4, 8 or 16 ones in a rectangle, as large and as few as possible, overlapping where needed, wrapping around the edges. Any incorrect loop caps the marks.
- Simplified sum-of-products [2]. One term per loop: the variables that do not change inside it. One mark for a correct term, one for all terms with the right operator and nothing extra. “Do not carry out any further simplification.”
- Simplest form [1]. Factorise with Boolean algebra: A.C + B.C = C.(A + B).
- Simplify using De Morgan’s laws and Boolean algebra [3–4]. One mark for the answer, the rest for naming and applying different laws. The Laws & rules tab lists every law as the mark scheme names it and checks your working line by line.
- Adders and flip-flops [1–8]. Name the circuit, complete its truth table with working, state the purpose of each output (Sum / Carry), draw an SR flip-flop from two NAND or NOR gates, know the invalid state and why the JK flip-flop fixes it, and that a flip-flop stores one bit.