Boolean Algebra - Logic Design

Question 1

Where can we have a minterm ,
and what is a minterm?

Answer 1

We can have a Minterm (Standard Product Term) when our expression is a SOP (Sum Of Products)
expression like this one:
f = x’y + xyz’ + xyz’w’
And the minterm here is the product term with all variables included in the term, so in this case:
xyz’w’ is our minterm

Question 1

When can we have a maxterm ,
and what is a maxterm ?

Answer 1

We can have a Maxterm (Standard Sum Term) when our expression is a POS (Products Of Sums) expression like this one:
f = (x + y)(x’ + z + y)
And the maxterm here is the one that has all the variables in the sum term. So in this case its (x’ + z + y).

Question 2

What are literals?

Answer 2

Literals are complement or non-complement variables used in the expression a literal can be: x, y’, z’ …

Question 3

What is a Product term ?

Answer 3

A product term can be a single literal x, y’ or many literals multiplied making one product term like this one: xy’, xy’z … etc.

Question 4

What is a Sum term?

Answer 4

A sum term can be a single literal x, y’ or sum of multiple literals like this one: (x + y’), ( x + y + z’) … etc.

Question 5

What can expressions be?

Answer 5

Expressions can be SOP (Sum of Products) OR gate example:
xy + z’y + xy’z.
Expressions can be POS (Product of Sums) AND gate example:
(x + y)(z’ + y)(x + y’ + z).
It can be both POS & SOP, example:
a + b’ + c + d’
we got 4 product terms, 1 sum term
[ ( a + b’ + c + d’) ] 4 variables and 4 literals.
It can be neither like this one:
a(b + c*d’) - > neither
4 variables, 4 literals, all we can say for this.

i.e.
But this a(b + c) this a sum term and this is a POS (a + 0)(b + c)
so 2 sum terms.