Problem Set #2:
Show your work!

1) Implement two bit integer multiplication with simplest circuits using Karnaugh maps.

Inputs are two two bit integers: A B and C D
Output is four bits that is the multiplied values: WXYZ

 A B
*C D
____
WXYZ

In class we showed that:
W = ABCD

For your reference, here are all the decimal values from 0 to 9 with their binary equivalents:

0000 = 0
0001 = 1
0010 = 2
0011 = 3
0100 = 4
0101 = 5
0110 = 6
0111 = 7
1000 = 8
1000 = 9

2) Implement two bit integer division (no fractional components). You
may list division by 0 as a don't care case.

Input are two two bit integers:
Output is the division:

 A B
/C D
____
 S T

Anything divided by 0 is a don't care.
Anything divided by 1 is itself.
Three and two divided 2 is 1, while all others divided by 2 are 0.
Three divided by 3 is 1 and all other numbers divided by 3 are 0.

Find S and T in simplest form. 


3) Design an SR flip flop using an And gate, an Or gate and some inverters.


4) Convert 37 into base 5.

5) Convert 23 from base 4 to hexadecimal.

6) Convert -17 into 6 bits two's complement.

7) Convert 17 into 6 bits two's complement.

8) Convert (10001000) from binary to hexadecimal.

9) Convert -3.375 into floating point.