Problem Generator

Generating a problem

The Generate a problem panel in the rail sets what you get:

• Difficulty — Warm-up: three inputs, two outputs, every condition stated plainly. Standard: four inputs and two outputs, the shape of a long-form homework item. Quiz · exam-style: four inputs, three outputs that lean on each other.
• Scenario — Surprise me, or pick a story.
• Required paths — which constructions the question asks for: 2-input gates, Line decoder + OR, Multiplexer, PLA.
• Seed — the same seed always generates the same problem. Share it and anyone you send it to works the identical problem; type one and press Use to open it.

Then press Generate a new problem.

Reading the question

The Problem tab sets the question like a printed quiz paper: notes on how it is marked, the story, and the questions with their points. The story mixes real signals with scenery — details that sound technical but decide nothing. Telling them apart is the first thing being tested.

The This problem panel counts its inputs, outputs, terms and gates once you have named the variables.

The nine-step walkthrough

The Walkthrough tab goes in the order a full answer is set out, and reveals nothing until you ask. Each step checks what you enter.

1. Sort out what is really a signal — inputs, outputs, and the scenery in between.
2. Name the variables and fix their order — your letters, your bit order. Short of time? Skip naming and use the suggested letters.
3. Translate every sentence into Boolean — word for word first, algebra second.
4. Fill in the truth table — every row, one output column at a time.
5. List the minterms — the canonical sum, before any simplification.
6. Group the ones on the K-map — biggest blocks first, wrap the edges.
7. Write the minimized expression — one product term per block.
8. Count the cost in 2-input gates — what the drawing has to contain.
9. Build it the ways the question demands — the required paths.

Steps 3 to 9 open once the variables are named. Open every step, Collapse all and Clear my answers sit above them.

Solve yours

Solve yours works a problem you already have — from a textbook, a past paper or a handout — step by step: the table, the minterms and maxterms, the map with its blocks, the minimal sum of products and product of sums, and what it costs to build. It reads:

• Equations, one per line, in any mix: F = A'B + C, F(A,B,C,D,E) = Σm(1,3,7) + d(5,6), G = ΠM(0,4). Each line is an output. Naming the variables in brackets fixes their order, and keeps one the expression leaves out.
• A truth table: rows of 0s and 1s, inputs first, with an optional heading row of names. 2ⁿ rows means n inputs, and every column after those is an output. X or - marks a don't-care.
• Words: one sentence per output saying when it is on, using and, or, not, either… or, neither… nor, unless, or a count — exactly one of, at least two of, a majority of, all of, none of. Sentences are read by a grammar, not understood, so check the table it shows.

Up to 8 inputs. Past four, the map splits into panes of sixteen, one for each value of the leading variables; a block that spans panes is drawn in each in the same colour. Don't-cares are taken as 1 only where that makes a block bigger. With several outputs, pick which one the steps work through.

Click any value in the table, or any cell of the map, to change it: 0, then 1, then X. Everything below is worked from the table, so a line read the wrong way is one click to put right. Save keeps the problem as you pasted it, and it opens solved again from Saved.

Three paths

One truth table, several circuits. The Three paths tab builds the answer each way the question asks: the way of the gate (2-input gates, with the count), the way of the decoder (a line decoder with an OR per output), the way of the multiplexer (n−1 select lines, the last variable as data) and the way of the PLA (a shared AND plane and an OR plane per output). In each schematic, the bold lines are the ones actually used.

The Method tab

The method behind the walkthrough, to read once and keep: how to take a problem apart, how to tell a signal from scenery, words that always mean the same gate, the K-map rules that actually cost marks, the laws worth memorizing, the construction paths side by side, where marks are lost, and the whole method worked in miniature on three variables.

Printing and saving

• Print the question sheet in the This problem panel prints the Problem tab as a paper quiz.
• Save (with a name) keeps a problem to come back to. A saved problem reopens with its own difficulty, scenario and paths. The sample project comes with one saved so you can see how it works.