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
1001 = 9
(you won't need the following, but it will be useful when we get to hex)
1010 = 10 = a
1011 = 11 = b
1100 = 12 = c
1101 = 13 = d
1110 = 14 = e
1111 = 15 = f
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.
(Take the existing design and try to push demorgan's law through it).
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 (101110100011) from binary to hexadecimal.
9) Convert -3.375 into floating point.
10) Convert (11000001011100000000000000000000) from floating point to decimal.