75 min read

Logic Practice Paper

Assignment-style questions: simplify three circuits and prove them with truth tables, then design a four-input control system — with a separate answer sheet.

About This Paper

This paper has two parts, like the logic task in a Computer Systems assignment. Part 1: write the expression for each circuit, simplify it with the laws of Boolean algebra, and check your answer with a truth table. Part 2: turn a written scenario into a truth table, Boolean equations and a circuit. Work on paper (or on your computer for practical tasks), just as you would in the real assignment. Show all your working. When you have finished, mark your work with the answer sheet .

Part 1 — Simplify and Check (3 circuits)

For each circuit: (a) label the gate outputs and write the Boolean expression for X; (b) simplify it, naming the law used on each line; (c) draw up a truth table with columns for the original and the simplified expression.

X = 0

Try it:

Circuit 1. You may click the inputs to explore it, but work out the expression on paper first.

Circuit 1 — inputs A, B, C

X = 0

Try it:

Circuit 2.

Circuit 2 — inputs p, q, r

X = 1

Try it:

Circuit 3.

Circuit 3 — inputs A, B, C

Part 2 — A Control System

(a) Make an input and output table. Say exactly what 1 means for each input, including thresholds. (b) Construct a truth table for the system, with columns for Y, A and F. (c) From the truth table, write a Boolean equation for each output. For Y, write the sum of products and then simplify it, naming the laws. (d) Draw a logic circuit to implement the sprinkler output Y, and circuits for A and F.

More lessons in Boolean Algebra and Logic Gates · Next: Logic Practice Paper: Answer Sheet · Previous: Logic Gates Worksheet

About This Paper

This paper has two parts, like the logic task in a Computer Systems assignment. Part 1: write the expression for each circuit, simplify it with the laws of Boolean algebra, and check your answer with a truth table. Part 2: turn a written scenario into a truth table, Boolean equations and a circuit. Work on paper (or on your computer for practical tasks), just as you would in the real assignment. Show all your working. When you have finished, mark your work with the answer sheet .

Part 1 — Simplify and Check (3 circuits)

For each circuit: (a) label the gate outputs and write the Boolean expression for X; (b) simplify it, naming the law used on each line; (c) draw up a truth table with columns for the original and the simplified expression.

X = 0

Try it:

Circuit 1. You may click the inputs to explore it, but work out the expression on paper first.

Circuit 1 — inputs A, B, C

X = 0

Try it:

Circuit 2.

Circuit 2 — inputs p, q, r

X = 1

Try it:

Circuit 3.

Circuit 3 — inputs A, B, C

Part 2 — A Control System

(a) Make an input and output table. Say exactly what 1 means for each input, including thresholds. (b) Construct a truth table for the system, with columns for Y, A and F. (c) From the truth table, write a Boolean equation for each output. For Y, write the sum of products and then simplify it, naming the laws. (d) Draw a logic circuit to implement the sprinkler output Y, and circuits for A and F.