ES1201
BEE-HOMEWORK 4
1)a)Find the 16's complement of B2FA
b)Convert B2FA to binary
c)Find the 2's complement of the result in part b
d) Convert the answer in c part to hexadecimal and compare it with answer in part a
(2)
(2)
2)a) The solutions to the quadratic equation (x^2) - 11x + 22 = 0 are x = 3 and x = 6. What is the base of
the numbers?
b)Convert the decimal number 431 to binary in two ways: (i) Convert directly to binary ii) Convert first
to hexadecimal and then from hexadecimal to binary. Which method is faster?
3)Draw logic diagrams to implement the following Boolean expressions:
(a) Y = A + B + B'(A + C')
(b) Y = A (B ⊕ D) + C'
(c) Y - A + CD + ABC
(d) Y = (A ⊕ C)' + B
(e) Y = (A' + B') (C + D')
(f)Y = [(A + B') (C' + D)]
(3)
4)For the Boolean function F = xy'z+x'y'z+w'xy+wx'y+wxy
(5)
(a)Obtain the truth table of F:
(b) Draw the logic diagram using the original Boolean expression.
(c)Use Boolean algebra to simplify the function to a minimum number of literals.
(d) Obtain the truth table of the function from the simplified expression and show that it is the same as the
one in part (a).
(e) Draw the logic diagram from the simplified expression, and compare the total number of gates with the
diagram of part(b)
5)Show that the dual of the exclusive-OR is equal to its complement.
(1)
6)Write the Output of the following circuits in a simplified form.
(2)
a)
b)
7)Simplify the following using k maps
(2)
a)w'z+xz+x'y+wx'z
b)c'd+a'b'c+abc'+ab'c
c)ab'c+b'c'd'+bcd+acd'+a'b'c+a'bc'd
d)xyz+wy+wxy'+x'y
(3)
8)Implement the following Boolean function F, using the two-level forms of logic (a) NANDAND, (b) AND-NOR, (c) OR-NAND
F= m(0,4,8,9,10,11,12,14)