DIGITAL DESIGN USING LOGIC.LY

TASK – PARITY CHECKER

TASK DESCRIPTION

In mathematics, the parity of a number refers to whether it is even or odd. Parity checks are used in computers to check if transferred data is corrupted or not. It is also useful when adding numbers.

In this circuit, we will look at how to create a circuit that checks the parity of any amount of bits (inputs).

THEORY

As opposed to checking the parity of a specific number (which is very simple in binary), we will be checking if the number of ones in a number is odd or even.

a) Two inputs

For two inputs, here is the truth table where 0 is given for even amounts of ones and 1 is given for odd amounts.

A B Q

0 0 0

0 1 1

1 0 1

1 1 0

This truth table is the same as the XOR gate. Therefore, A XOR B = Q

b) Three inputs

Let’s consider the truth table for three inputs.

A B C Q

0 0 0 0

0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0

1 1 1 1

While it might not be clear, this truth table is equal to A XOR B XOR C = Q.

c) Four inputs

A B C D Q

0 0 0 0 0

0 0 0 1 1

0 0 1 0 1

0 0 1 1 0

0 1 0 0 1

0 1 0 1 0

0 1 1 0 0

0 1 1 1 1

1 0 0 0 1

1 0 0 1 0

1 0 1 0 0

1 0 1 1 1

1 1 0 0 0

1 1 0 1 1

1 1 1 0 1

1 1 1 1 0

Again, if you inspect this, you will see that A XOR B XOR C XOR D = Q.

PATTERN

The pattern continues indefinitely. We can simply add more and more XOR gates for each input.

TASK

Create a 3-input parity checker for a max mark of 80 %; or

Create a 4-input parity checker for a max mark of 90 %; or

Create a 5-input parity checker for a max mark of 100 %.

Test all input values to make sure that your circuit is correctly stating the parity of the inputs.

Remember to label your inputs and your outputs. Square your wires. Be neat!

TO SUBMIT

One screen capture of your circuit.