Derive the Boolean expression for the logic circuit shown.
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Boolean Algebra Expressions can be used to construct digital logic truth tables for their respective functions
As well as a standard Boolean Expression, the input and output information of any Logic Gate or circuit can be plotted into a standard table to give a visual representation of the switching function of the system.
The table used to represent the boolean expression of a logic gate function is commonly called a Truth Table. A logic gate truth table shows each possible input combination to the gate or circuit with the resultant output depending upon the combination of these input(s).
For example, consider a single 2-input logic circuit with input variables labelled as A and B. There are “four” possible input combinations or 22 of “OFF” and “ON” for the two inputs. However, when dealing with Boolean expressions and especially logic gate truth tables, we do not general use “ON” or “OFF” but instead give them bit values which represent a logic level “1” or a logic level “0” respectively.
Then the four possible combinations of A and B for a 2-input logic gate is given as:
Input Combination 1. – “OFF” – “OFF” or ( 0, 0 )
Input Combination 2. – “OFF” – “ON” or ( 0, 1 )
Input Combination 3. – “ON” – “OFF” or ( 1, 0 )
Input Combination 4. – “ON” – “ON” or ( 1, 1 )
Therefore, a 3-input logic circuit would have 8 possible input combinations or 23 and a 4-input logic circuit would have 16 or 24, and so on as the number of inputs increases. Then a logic circuit with “n” number of inputs would have 2n possible input combinations of both “OFF” and “ON”.