Question

Consider the following truth table, where I3, I2, I1, and I0 are the inputs and Y3, Y2, Y1, and YO are the outputs,

a) Find the minimal SOP forms of Y3 and Y2 only
I3 I2 I1 Io Y3 Y2 Y1 Yo
0 0 0 0 0 0 0 1
0 0 0 1 0 0 1 0
0 0 1 0 0 0 1 1
0 0 1 1 0 1 0 0
0 1 0 0 0 1 0 1
0 1 0 1 0 1 1 0
0 1 1 0 0 1 1 1
0 1 1 1 1 0 0 0
1 0 0 0 1 0 0 1
1 0 0 1 1 0 1 0
1 0 1 0 1 0 1 1
1 0 1 1 1 1 0 0
1 1 0 0 1 1 0 1
1 1 0 1 1 1 1 0
1 1 1 0 1 1 1 1
1 1 1 1 0 0 0 0

Answer 1

The minimal SOP form of Y3 can be found by examining the truth table, and the same process can be used to find the minimal SOP form of Y2.

Step-by-step explanation:

The minimal SOP (Sum-of-Products) form of Y3 can be obtained by examining the truth table for when Y3 is true (1). It can be seen that Y3 is true when (I3' * I2' * I1' * I0') or (I3' * I2' * I1 * I0) or (I3' * I2 * I1 * I0').

The minimal SOP form of Y2 can be obtained in a similar manner. It can be seen that Y2 is true when (I3' * I2' * I1 * I0') or (I3' * I2' * I1 * I0) or (I3' * I2 * I1' * I0).

The student is asked to find the minimal Sum of Products (SOP) forms of outputs Y3 and Y2 based on a given truth table. To find the SOP for Y3, we look at all the instances where Y3 is 1. Similarly, for Y2 we gather all instances where Y2 is 1 and write the corresponding minterms. We then simplify the minterms using Boolean algebra or Karnaugh Maps to find the minimal SOP form.