2.4 Representation and Implementation of Logic Function
Ways of representing and implementing logic functions:

· Boolean expression

· Truth table

· Logic circuit

A logic function in the form of a Boolean expression is a mathematical statement formed with binary variables, operators OR, AND, and NOT, parentheses, and an equal sign. For a given value of the variables, the function can be either 0 or 1. This algebraic expression is manipulated with the use of Boolean algebra to come up with simpler expression for the same function.

Any logic function can be represented in a truth table. The number of rows in the table is 2ⁿ where n is the number of binary variables in the function.

A logic function is transformed from an algebraic expression into a logic circuit or diagram. It is implemented using the logic gates previously discussed.

Figure 1. Ways in representing logic functions

Figure 1 depicts how different representations of logic functions are interconnected. The diagram's arrows indicate that if you have one form of a logic function, you can derive the other two. For instance, if you're given a logic function (like a Boolean expression), you can create its truth table and design its logic circuit. Conversely, if you start with a truth table, you can determine the logic function and then build the circuit. Finally, if you have an existing logic circuit, you can work backward to find its Boolean expression and construct its truth table.

Example No. 1

Obtain the logic circuit and truth table for the function:

F=x+y’z

Solution.

The logic function F=x+ y’z means that F will equal to 1 if x=1 regardless of the value of y and z, or F = 1 if y=0 and z=1, regardless of the value of x.

Figure 2. Logic Circuit of F=x+y'z

X	Y	Z	F
0	0	0	0
0	0	1	1
0	1	0	0
0	1	1	0
1	0	0	1
1	0	1	1
1	1	0	1
1	1	1	1