Boolean algebra deals with binary number system. It is very useful in designing logic circuits used in processors of computer system. In this chapter, you will learn about this algebra and elementary logic gates used to build up logic of all circuits in a computer. You will also learn how to use Boolean algebra for designing simple logic circuits used frquently by arithmetic logic unit if almost all computers.
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 )