CMPT 150
Truth Table to Functions
Page 1
Counting Boolean Functions
box5
How many truthtable rows for a function of
n
variables?
box5
box5
How many unique
n
variable functions are there?
box5
I.e. how many unique outputs are there for a function of
n
variables?
box5
box5
For example,
CMPT 150
Truth Table to Functions
Page 2
Going from Truth Table to a
function
box5
Identify the minterms
box5
Combination of variables in table (e.g. row)
box5
For example:
f(x,y,z) = (xy
’
z + xy)
⊕
z
x
y
z
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
box5
One simple way to express the truth table is to use
∑
to list the 1valued minterms
CMPT 150
Truth Table to Functions
Page 3
Minterms
box5
There are many different algebraic functions that
represent the same function
box5
They are the same
iff
they have the same truth table
box5
We can use truth tables to systematically find a minimal
representation of a function in algebra
box5
We can easily convert a truth table into a
sum of
products
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 Spring '08
 Dr.AnthonyDixon
 Boolean Algebra, Karnaugh map, Canonical form

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