[SOLVED] Octal to Binary encoder (equations from truth table)

[Eshal]

Hello experts!

Here is a attached diagram of the truth table of the Octal-to-Binary encoder and its equation which is extracted from the truth table and then last is the implementation of the equation.


How did they drive equation from the truth table. It is not the SOP equation. Then how did they get it?
Thank you

 

[gursharanjeetkalra]

Hello experts!

Here is a attached diagram of the truth table of the Octal-to-Binary encoder and its equation which is extracted from the truth table and then last is the implementation of the equation.
View attachment 90109

How did they drive equation from the truth table. It is not the SOP equation. Then how did they get it?
Thank you

Equations are derived from the truth table as:
For Y2: It is 1 for conditions I4 or I5 or I6 or I7 is 1. (See inputs from I0 to I7)
For Y1: It is 1 for I2 or I3 or I6 or I7 is 1. (See inputs from I0 to I7)
For Y0: It is 1 for I1 or I3 or I5 or I7 is 1. (See inputs from I0 to I7)
Hope it will work.

 

[Eshal]

Thank you very much.