Write the base 10 numbers 0 through 15 in base 2 Say Fw x y

Write the (base 10) numbers 0 through 15 in base 2. Say F(w, x, y, z) = 1 iff the number (wxyz)_2 is divisible by 2 and 3 and G(w, x, y, z) =1 iff the number (wxyz)_2 is divisible by 2 or 3. Find minimal expressions for F and G. Draw their circuit diagrams.

Solution

F will have all multiples of 6 as 6,12,18......

G will be of the form 2,3,6,8,9............

F is a subset of G

Base 10	Base 2
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010
11	1011
12	1100
13	1101
14	1110
15	1111