.logic functions

1. Logic functions
By
Md. Fazle Rabbi
16CSE057

2. 4.2
Logic functions
• Variables with only two values are called
Logic variables or Switching variables
• We defined several Boolean/Logic operators
• A large variety of situations and problems
can be described using logic variables and
logic operators.
• The description is done through logic
functions

3. 4.3
Properties of logic functions
• If F1(A1, A2, ... An ) is a logic function, then (F1(A1,A2,
... A n))/ is also a Boolean function.
• If F1 and F2 are two logic functions, then F1+F2 and
F1.F2 are also Boolean functions.
• Any function that is generated by the finite application
of the above two rules is also logic function
There are a total of 2 distinct logic functions of n
variables

4. 4.4
Terms to get familiarized
• Literal: not-complemented or complemented version
of a variable (A and A/ are literals)
• Product term: A series of literals related to one
another through an AND operator.
Ex: A.B/.D, A.B.D/.E, etc.
• Sum term: A series of literals related to one another
through an OR operator.
Ex: A+B/+D, A+B+D/+E, etc.

5. 4.5
Truth Table
• It is a tabular representation of a logic
function.
• It gives the value of the function for all
possible combinations of the values of the
variables
• For each combination, the function takes
either 1 or 0

6. 4.6
Simpler Truth Table
F = A.B.C.D/.E/ + A.B/.C.D/.E + A/.B/.C.D.E + A.B/.C/.D.E

7. 4.7
English Sentences Logic Functions
Anil freaks out with his friends if it is Saturday and he
completed his assignments
• F = 1 if Anil freaks out with his friends; otherwise F = 0
• A = 1 if it is Saturday; otherwise A = 0
• B = 1 if he completed his assignments; otherwise B = 0
• F is asserted if A is asserted and B is asserted.
The sentence, therefore, can be translated into a logic
equation as
F = A.B

8. 4.8
Minterms
• A logic function has product terms.
• Product terms that consist of all the variables of
a function are called "canonical product terms",
"fundamental product terms" or "minterms".

9. 4.9
Maxterms
• Sum terms which contain all the variables
of a Boolean function are called "canonical
sum terms", "fundamental sum terms" or
"maxterms".
• (A+B/+C) is an example of a maxterm in a
three variable logic function

10. 4.10
Minterms and Maxterms of 3 variables

11. 4.11
Logic function as a sum of minterms
Consider a function of three variables
F = m0 + m3 + m5 + m6
This is equivalent to
F = A/B/C/ + A/BC + A/BC/ + ABC/
A logic function that is expressed as an OR of several
product terms is considered to be in "sum-of-
products" or SOP form.

12. 4.12
Logic function as a product of Maxterms
F is a function of three variables
F = M0 . M3 . M5 . M6
When F expressed as an AND of several sum
terms, it is considered to be in "product-of-sums"
or POS form.

13. 4.13
Canonical form
If all the terms in an expression or function are
canonical in nature, then it is considered to be
in canonical form.
• minterms in the case of SOP form
• maxterms in the case of POS form

14. 4.14
Canonical form
Consider the function
F = A.B + A.B/.C + A/.B.C
It is not in canonical form
It can be converted into canonical form:
A.B = A.B.1
= A.B.(C + C/)
= A.B.C + A.B.C/
The canonical version of F
F = A.B.C + A.B.C/+ A.B/.C + A/.B.C

15. 4.15
Priorities in a logical expression
• NOT ( / ) operation has the highest priority,
• AND (.) has the next priority
• OR (+) has the last priority