Any decision which results into a YES (TRUE) or NO (FALSE) is called a binary decision.
• Logical function or Compound statement. Algebraic variables like a, b, c, x, y etc. are combined with help of mathematical operators like +,-,x,/. Similarly, logical statements or truth functions are combined with help of logical operators to form a logical function. For example :He prefers tea not coffee. He plays piano and she plays sitar. On Sundays, I watch TV or go for swimming. The AND, OR, NOT are the logical operators.
• Logical operators
A truth table is a table which represents all the possible values of logical variables along with all possible results of given combinations of values.
Logical variables are combined by means of logical operators to form Boolean expression. For example-
o X + YZ’ + Z
o Y’ + Z’
Boolean expressions are evaluated by constructing the truthtable. Consider the expression- X + (Y.Z)’ To study this expression, first consider all the combinations of X, Y and Z. total number of combinations for 3 variables is 23 = 8.
• If X = 0 then X = 1 and if X = 1 then X = 0
• Logical addition (OR relations)
• Logical multiplication (AND relations)
• Complement rules (NOT relations)
( The Tutorial document contains more elaborate explanations on how these theorems can be explained using truth tables or otherwise. )
Proof— These properties can be proved by creating a truth table as will be shown in the tutorial.
(X’)’ = X
Moving on beyond the outline, here's the complete tutorial with examples, truth tables and problems :
Here's a list of all the tutorials we currently have in this area - Introductory Digital Electronic Circuits and Boolean logic
Tutorials in Basic Digital Electronics: At a glance