This preview shows page 1. Sign up to view the full content.
Unformatted text preview: be made so by first expanding the expression into a sum of AND
terms. Each term is then inspected to see if it contains all the variables. If it misses one or
more variables, it is ANDed with an expression of the form (x + x), where x is one of the
missing variables. The following example clarifies this procedure.
Example 6.4. Express the Boolean function F = A+ BC in the sumofminterms (products) form.
Solution:
The function has three variables A, B and C. The first term A is missing two variables,
therefore
A = A • (B + B) = AB + AB
This is still missing one variable, therefore
A = A • B • C+C) + A•B• (C+C)
=A•B•C•+A•B•C+A•C+A•B•C
The second term B • C is missing one variable, therefore
B • C = B • C • (A+A)
= A • B • C+ A • B • C
Hence by combining all the terms we get
F = A•B•C + A•B•C +A•B • C + A•B • C +A•B • C+A •B • C
But in the above expression, the term ABC appears twice and according to theorem l(a)
we have x + x = x. Hence it is possible to remove one of them. Rearranging the minterms
in ascending order, we finally obtain:
F=A•B•C+A•B•C+A•B•C+A•B•C
= m1 m4 + m5 + m6 + m7
It is sometimes convenient to express the Boolean function, when in its sumofminterms,
in the following short notation:
F(A,B,C) = Z(1,4,5,6,7)
The summation symbol 'Z' stands for the ORing of terms. The numbers following it are
the minterms of the function. Finally, the letters in parentheses with F form a list of the
variables in the order taken when the minterm is converted to an AND term.
ProductofSums
A productofsums expression is a sum term (maxterm) or several sum terms (maxterms)
logically multiplied (ANDed) together. For example, the expression (x +y)(x+ y) is a
product of sums expression. The following are all productofsums expressions:
x
(X+y)
(x + y)z
(x+ y)(x+y)(x + y)
(x + y)(x+y + z)
The following steps are followed to express a Boolean function in its productofsums
form: 1. Construct a truth table for the given Boolean function.
2. Form a maxterm for each combination of the varibles which produce a 0 in the
function.
3. The desired expression is the product (AND) of all the maxterms obtained in s...
View
Full
Document
This document was uploaded on 04/07/2014.
 Spring '14

Click to edit the document details