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6.10 Deriving Boolean functions from truth tables
A Boolean function can be represented in the form of a truth table and sometimes it becomes necessary
to necessary to convert a truth table to a product of sum or sum of products form.
Consider the truth table below:
A B F
0 0 0
0 1 1
1 0 1
1 1 1
To convert this truth table to a Boolean function, the following steps need to be followed:
• Note where F =1 in the truth table and write the input combination
• If F= 1 in more than one instance, the input combinations of the respective outputs are joined by
an OR(+) sign
• Simplify the formed Boolean function if it is complex
In the above truth table F = 1 in three instances, so the Boolean expression can be written as:
F = AB + AB + AB
= AB + A(B + B)
= AB + A = A + AB
= A + B
Consider the truth table below:
A B F
0 0 1
0 1 1
1 0 1
1 1 0
F = AB + AB + AB
= A(B + B) + AB
= A + AB
= A + B
Consider the truth table below:
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