Question 3 - 4 in the PDF file

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Homework #2
CSE140
Prof. Tajana Simunic Rosing
1. Simplify the expression using K-Maps.
(a) F(a, b, c) = ∑(1, 2, 3, 6, 7)
(b) ab + a’b’c’ + a’bc’
2.
(a) Simplify the following expressions to minimal sum-of-products form using boolean
algebra. Verify using K-Map. (a’ + c + d)(b + c + d)(a + b + c’) HINT: Use consensus
theorem.
(b) Simplify the following expressions to minimal product-of-sums form using boolean
algebra. Verify using K-Map. a’c+a’b’d+cd’.
NOTE: You do not need to mention the name of any theorem or axiom used.
3. Logic minimisation using k-maps
a. A bulb in the staircase has 3 switches. The bulb is turned ON for the following
state of the switches.
● Switch A is ON, Switches B,C are OFF
● Switch C is ON, Switches A,B are OFF
● Switches B,C are ON, Switch A is OFF
● Switches A,C are ON, Switch B is OFF
Answer the following questions for the above problem
i.
Give the truth table
ii.
Give expression for output in canonical sum of products form
iii.
Minimize the output expression obtained in part ii using k-map
iv.
Draw the logic circuit for the minimized equation from part iii using any
logic gates
b. Determine the minimized SOP a
​ nd ​POS expression of the following function
using k-maps f (A, B, C , D) = ∑m (4, 6, 8, 10, 11, 15) + ∑d (3, 5, 7, 9)
4. Determine whether the two following circuits are equivalent using Boolean algebra.
Circuit 1: Circuit 2:

Attachments:

• 1493944064-HW2.pdf