Solutions to Exercises in Digital Electronic Systems Unit 6

Solution – (Ex. 1)

The terms to which De Morgan’s theorems are applied are identified.

Assign

Then

Solution – (Ex. 2)

Solution – (Ex. 3)

The terms to which De Morgan’s theorems are applied are identified.

Assign

Recalling that

This yields

Now De Morgan’s Theorem is applied to the second term, as the first term cannot be minimised any further.

Assign

Recalling that

1

Solutions to Exercises in Digital Electronic Systems Unit 6

This yields

The overall function is

This can be rewritten in Sum of Products (SOP) form by applying the distribution rule

Solution – (Ex. 4)

As before we select the X and Y terms for application of De Morgan’s Theorem.

Recalling that

Thus

Now we apply De Morgan’s theorem to each of the terms in the brackets

This is the function expressed in Sum of Products (SOP) form.

Solution – (Ex. 5)

2

Note where line is split

Solutions to Exercises in Digital Electronic Systems Unit 6

Solution – (Ex. 6)

Solution – (Ex. 7)

Say

Then

Note: For simplification of the term, an alternative method may be employed.

Say

Then

3