This says its having two 2bit inputs so how to find the truth table

Question

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

Answer 1

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.