Now you should find it easy to solve the following exercise E4 Simplify tlie Boolean expression X X1 X2 X3 x1 A X2 V X1 AX2 A X3 V X2 AX3 With this we conclude this section In the next Section we shall give an important application of the concepts discussed here 3 4 LOGIC CIRCUITS If you loole around you would notice many electric or electronic appliances of daily use Sorne of them need a sirnple switching circuit to control the auto stop such as in a stereo system Some would use an auto power oil systeni used in transformers to control voltage fluctuations Each circuit is usually a combination of on off switches wirecl together in some specific configuration Nowadays certain types of electronic blocks i e solid state devices such as transistors resistors and capacitors are more in usc We call these electronic bloclcs logic gates or simply gates In Fig 5 we have shown a box which consists of some electronic switches or logic gates wired together in a specific manner Each line which is entering tlie box from the left represents an independent power source called input where all of them need not supply voltage to tlie box at a given moment A single line coming out of the box gives tlie final output of the circuit box The output depends on the type of input Input power lines Circuit Box Output lead Fig 5 A logic circuit This sort of arrangement of input power lines a circuit box and output lead is basic to all electronic circuits Throughout tlic unit any sucli interconnected assemblage of logic gates is referred to as a logic circuit As you may know computer hardwares are designed to handle only two levels of voltage both as inputs as well as outputs These two levels denoted by 0 and 1 are called bits an acronym for binary digits When the bits are applied to the logic gates by means of one or two wires input leads tlie output is again in the form of voltages 0 and 1 Roughly speaking you may think of a gate to be on or off according to whether the output voltage is at level 1 or 0 respectively Three basic types of logic gates are an AND gate an OR gate and a NOT gate We shall now define them one by one Definition Let the Boolean variables x and x2 represent any two bits An AND gate receives inputs x arid x2 and produces the output denoted by xi A x2 as given in Table 3 alongside The standard pictorial representation of an AND gate is shown in Fig 6 From the first three rows of Table 3 you can see that whenever the voltage in any one of the input wires of the AND gate is at level 0 then the output voltage of the gate is also at level 0 Boolean Algebra a Circu Table 3 Output X1 0 0 AND gat X2 X1 X2 0 0 1 1 0 0 0 1