Q1) Convert the following numbers from the given base to the other three bases listed in the table. Show all your work.
Decimal: 45.0625
Binary: 101101.0001
Hexadecimal: 2D.1
Octal: 55.1
Base 8: 101.11
Binary: 1101.001
Hexadecimal: D.2
Decimal: 5.375
Base 16: F4.2
Binary: 11110100.0010
Octal: 364.1
Decimal: 244.125
Base 10: 143
Binary: 10001111
Hexadecimal: 8F
Octal: 217
Q2) Simplify the following Boolean expressions to a minimum number of literals.
a) ABC + ABC + ABC
b) xyz + xyz + wxy + wxy + wxy
c) xy + xy + yz
Q3) If the minimized expression of a function F is given as F(A,B,C,D) = A * B + C + D, then
a) Provide the truth table of the function F(A,B,C)
b) Find all the minterms of the function F(A,B,C)
c) Find all the maxterms of the function F(A,B,C)
Q4)
a) Obtain the minimal sum-of-product expression for the logic function given below.
Fx,y,z = m0,4,5 (Hint: these are minterms)
b) Obtain the minimal product-of-sums expression for the logic function given in part (a).
c) Obtain the minimal sum-of-products expression for the logic function given below, where d indicates don't cares.
FA,B,C,D = m3,6,7,8,10,14,15 + d1,4,5,13 (Hint: these are minterms and don't cares)
d) Obtain the minimal product-of-sums expression for the logic function given in part (c).
