Producing K map using two numbers

Question

I have found this problem in my textbook.

The system has 3 inputs. The first two, A and B, represent a number in the range 0 to 2 (3 is not used). The third input, C represents a second number in the range 0 to 1. The output, f, is to be 1 if and only if the two numbers equal to each other.

(1) Create the truth table of the system.

(2) Create the k-maps of the system

(3) Get the express f(A, B, C) in minimum SOP form.

(4) Get the express f(A, B, C) in minimum POS form.

I have tried this way:

c A B f

0 0 0 1

0 0 1 0

0 1 0 0

0 1 1 x

1 0 0 0

1 0 1 0

1 1 0 0

1 1 1 x

As f=1 when AB == C .

What does it mean by "The output, f, is to be 1 if and only if the two numbers equal to each other." ? What will be the truth table?

Answer 1

What does it mean by "The output, f, is to be 1 if and only if the two numbers equal to each other." ?

All that means is that AB == C, then f=1. So if AB=1 & C=1, f=1. Same thing happens if AB=0 & C=0, f=1.

So from the question, I gathered that 0 to 2 means that you have A and B in terms of Binary as 00, 01, 10, and 11 is a don't care. With that being said, the truth table would look as follows:

• AB | C | f
• 00 | 0 | 1
• 01 | 0 | 0
• 10 | 0 | 0
• 11 | 0 | X
• 00 | 1 | 0
• 01 | 1 | 1
• 10 | 1 | 0
• 11 | 1 | X

You can very easily extract the K-maps parameter from the truth table as it is essentially the same thing.