Now let us discuss about 3x8 decoder. In this video we are mainly going to discuss about the block diagram of a 3x8 decoder as well as truth table and logic circuit. First let's see what is a 3x8 decoder.
A 3x8 decoder has 3 inputs and 8 outputs. Let's see the block diagram. This is the block diagram.
A 3x8 decoder accepts 3 inputs. such as a b and c and it produces eight outputs such as y naught y 1 y 2 y 3 y 4 y 6 and y 7 in addition to the three inputs here we have another input called e e stands for enable input okay if the enable input is active then only the decoder produces the output suppose if the enable input is deactivated if the enable input is low then it doesn't produces any outputs here 3 by 8 decoder is called as many input many output circuit why because it accepts many number of inputs and it produces many number of outputs so a 3 by 8 decoder decodes converts three input lines into eight output lines okay uh next let us see the truth table for the 3 by 8 decoder so here we have three inputs such as abc in addition to the three inputs we have e enable input and it produces eight outputs from y naught to y7 if the enable input is low if the enable input is deactivated that means if the enable input is 0 then irrespective of the inputs it doesn't produces any outputs so here x means don't care so the inputs may be either 0 or 1 but it doesn't produces any outputs okay next if the enable input is 1 then only it produces the output so first combination triple zero so if the inputs are triple zero then what will happen is the first output line That is y0 will be active. So what is the, now y0 will become 1. So remaining combinations y1, y2, y3, y4, y6, y7, 0. So now we can write y0 as, when y0 is 1, then what is the combination? 0, 0, 0. So a bar, b bar, c bar.
So y0 equal to a bar, b bar, c bar. Likewise, when the inputs are 0, 0, 1. then the second output line will become active so we will get output as the second output line what is the second output line y1 so now y1 will be active y1 this is y1 y1 will be active whereas the remaining lines are inactive so when y1 is 1 then what is the combination 0 0 1 so that means a bar b bar c so y1 equal to a bar b bar c likewise when the inputs are 0 1 0 then y2, the third output line will be active. What is the third output line?
y2. y2 will be active. When y2 is 1, then what is the combination, input combination? 0, 1, 0. So, what is 0, 1, 0?
a bar, b, c bar. So, y2 equal to a bar, b, c bar. So, likewise, when the inputs are 0, 1, 1, then the fourth output line will be active.
What is the fourth output line? y3. y3 will be active.
so when y3 is active then what is the input combination 0 1 1 so a bar b c a bar b c next likewise we can write for the remaining combinations so y4 equal to y4 equal to a b bar a a b bar c bar next to y5 equal to a b bar c a b bar c y6 equal to a b y6 equal to a b c bar y7 equal to abc now let us see the logical circuit so here we require first line input line enable input line and next input line a and we may get a bar also okay so for bar use not gate so this line represents a bar so next in next line next input line b next not it represents b not next line c so next line c next line c bar okay you so let us derive the formula let us derive the circuit for y naught y naught equal to so we can write as a bar b bar c bar into e into e so we can write e here why because when the enable input is active so then only we will get the output okay so e a bar b bar c bar so this is e line so this is this line represents a bar this line represents b bar this line represents c bar so this is nothing but why not if you perform under operation on e a bar b bar c bar b bar a bar next line is b bar next line is c bar then we will get y naught so likewise let us derive the remaining also y 1 equal to e a bar b bar c a y 1 equal to e a bar b bar c so this is nothing but y 1 next let us derive one more y 2 equal to e a bar b c bar so e a bar next b c bar so this is b and this is c bar okay this is c bar okay so likewise we can derive for y3 y4 y5 y6 what is the last one y7 equal to e a next b and c so this line is nothing but c so this is nothing but yc so this is nothing but the logical circuit for the 3 by 8 decoder so this is about 3 by 8 decoder