Basic Digital Techniques & Applications - PART 2

23:41:00 Nandan Bhalwankar 0 Comments

Boolean Algebra:

As the name suggests, it works with Boolean logic (1 or 0 i.e. true or false). Boolean algebra is a system of mathematical logic, a two-valued (1 and 0) switching algebra.It can also be said as the rules for manipulation of binary variables. In spite of this, it is different from both ordinary algebra and binary number system.

As an example,

In ordinary algebra 1 + 1=2. But in Boolean Algebra, 1+1 = 10 (Decimal 2)

Operations of Boolean Algebra:

Basic operations of Boolean Algebra are as follows:

1) AND (conjunction):

If we consider 2 variables as A and B, then this operation is represented as – ‘A AND B’. Since there are two Boolean variables (A and B) and two values (0 and 1) that these variables can hold, there are 4 possible combinations. These combinations are as follows:

The first diagram above is the AND gate.  There are two input lines, namely A and B, Y is the single output line. The ‘AND’ operation is denoted by a dot (.), hence Y is written as Y = A . B. The operation can also be written as Y = A AND B.

The table has two columns A and B. These are input lines. As said, there can be 4 possible combinations of these values. The output of each combination is shown in the last column. Such a table is called as a ‘Truth Table’.

2) OR (disjunction):

This operation is represented as plus sign (+). If we consider 2 variables as A and B, then this operation is represented as – ‘AORB’. Since there are two Boolean variables (A and B) and two values (0 and 1) that these variables can hold, there are 4 possible combinations. These combinations are as follows:

3) NOT (negation):

This operation is represented as a bar on the top of the variable. Consider variable‘A’, then this operation is represented as – ‘NOT A’. Since it’s a Boolean variable and two values (0 and 1) that these variables can hold, there are 2 possible combinations. These combinations are as follows: