And Operation (10th-Physics-Lesson-19.12)

In order to understand AND operation, we consider input variables A and B as two switches. There are four possible sates of these two switches which are given below:

1. Both A and B are open                                                          i.e., A = 0, B = 0
2. The switch A is closed and B is open                                i.e., A = 1 , B = 0
3. The switch A is open and B is closed                                i.e., A = 0, B = 0
4. Both switches A and B are closed                                       i.e., A = 1, B = 1

Table 19.1

The four possible states of the switches A and B are given in table 19. 1. A circuit is formed by connecting these two switches in series as shown in fig. 19.17. Whether a current would pass through the circuit or not, it depends upon the state of the switches. In this circuit A and B are two input variables. Whereas the current passing trough the circuit is the output variable X. its values would be 1 when bulb connected in circuit glows showing that current is passing through the circuit. But the value of X would be 0 when the current through the circuit does not flow and the bulb would not glow.

Now we would find out the value of the output X for all possible values of the input variables A and B as given in table 19.1.

1. In the first line of the table A = 0, B = 0, i.e., both the switches are open (fig. 19.17). in this condition, no current would pass through the circuit, so the value of X would be 0.
2. In second line of the table, a = 1, B = 0, i.e., switch A is closed and B is open (fig. 19. 18). Even in this condition no current would pass trough the circuit and X = 0.
3. In third line of the table A = 0, B = 1 i.e. switch A is open and B is closed (fig. 19. 19). No current would pass through the circuit, i.e. X = 0.
4. In fourth line of the table A = 1, B = 1 i.e. both the switches are closed (fig. 19.20). Now the current would pass through the circuit and bulb would glow. Thus X would be 1 in this case. The value of X for the various values of the Boolean variables A and B is shown in table 19.2. Whenever two Boolean variables operate in such a way as two witches are connected in series, then their operation is said to be AND operation. So we can define the operation is said to be AND operation. So we can define the AND operation to be such a logic operation that its output is 1 only when all the values of its inputs are 1. It is presented by the sigh of multiplication or by a dot. Thus the output X obtained as a result of AND operation shown in table 19.2 is written as X = A.B.
5. 

Table 19.2

It is read as “X equal A AND B”. Table 19.2 is called as the truth table of and operation. Truth table shows all the values of the input variables and the value of out put for each set of the values of the inputs. By using the sign of and operation, the various lines of the truth table can be written as in table 19.3. The various operations of Boolean variables are called as logic operations because the various variables used in subject of logic also possess two values. The word “truth” has also been borrowed from this subject.

In digital electronic, the 0 and 1 values of the variables are simulated by two different levels of the potential. Usually 0 is represented as zero or ground potential and 1 by 5 volts or by any other suitable voltage. Then such circuits have been designed which implement the various logic operations. These circuits are known as logic gates.

The circuit which implements the AND operation is known as and gate. Its symbol is shown in fig. 19.21. It has two or more than two inputs and only one output. It operates is such a fashion that the value of its output is always in accordance with the truth table of and operation; i.e., the value of its output is only 1 (5volts) when all of its inputs are at 1 (5 volts). For all other values of the inputs the output would be zero.

Table 19.3