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1. A 4-bit non-prime number detector (output 1 for non-prime numbers).
Suppose the input number is ABCD, the output function is F.
(1) Draw the truth table
Decimal
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
A
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
B
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
C
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
D
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
F
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
(2) Simplify with K-map
AB
00
01
11
10
00
1
1
1
1
01
1
0
0
1
0
0
1
0
0
1
1
1
CD
11
10
F  BC  BD　 AD　 ABC
All are essential prime
implicants
2. Suppose a BCD number X = ABCD, design a function F such that
if X mod 3 = 0
then F: = 0
else F: = 1;
(1) Draw the truth table
Decimal
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
A
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
B
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
C
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
D
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
F
0
1
1
0
1
1
0
1
1
0
X
X
X
X
X
X
(2) Simplify with K-map
AB
00
01
11
10
0
1
X
1
CD
00
01
11
10
All are essential prime
implicants
1
1
X
0
0
1
X
X
1
0
X
X
F  BC　 BD  A CD  BCD　 AD　
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