Question 2
A logic circuit is given two 2-bit binary numbers A and B as its inputs. The circuit consists of two outputs Y1 and Y2. The output values of YI and Y2 are obtained as follows:
If A<B, then Y1 and Y2 will be equal to A-B. Else Y1 and Y2 will be equal to A
a) Determine the truth table for the system
b) Obtain the simplified:
i SOP for Y1 and Y2.
ii. POS expressions for YI
Truth Table:
A1 A2 A B1 B2 B A<B? Y1=Y2=A-B||A Y11-Y21 Y12=Y22 Y13=Y23
0 0 0 0 0 0 n 0 0 0 0
0 0 0 0 1 1 y -1 1 1 1
0 0 0 1 0 -1 n 0 0 0 0
0 0 0 1 1 -2 n 0 0 0 0
0 1 1 0 0 0 n 1 0 0 1
0 1 1 0 1 1 n 1 0 0 1
0 1 1 1 0 -1 n 1 0 0 1
0 1 1 1 1 -2 n 1 0 0 1
1 0 -1 0 0 0 y -1 1 1 1
1 0 -1 0 1 1 y -2 1 1 0
1 0 -1 1 0 -1 n -1 1 1 1
1 0 -1 1 1 -2 n -1 1 1 1
1 1 -2 0 0 0 y -2 1 1 0
1 1 -2 0 1 1 y -3 1 0 1
1 1 -2 1 0 -1 y -1 1 1 1
1 1 -2 1 1 -2 n -2 1 1 0
Y11-Y21 K-MAP (Karnaugh map):
A1A2\B1B2 0 0 0 1 1 1 1 0
0 0 0 1 0 0
0 1 0 0 0 0
1 0 1 1 1 1
1 1 1 1 1 1
Y11-Y21 Sum Of Products:
A1 V (A1' ^ A2' ^ B1' ^ B2)
Y11-Y21 Product Of Sums:
(A1 v A2')^(B1' v A1)^(A1 v B1 v B2)
The rest is left was an exercise or for another Answerer.
