MID-SEMESTER EXAMINATION - Solutions
Question 1: (6 marks)
To prepare his mind about the ensuing state elections, a voter wants to record all the
information he has about the candidates in terms of binary variables as follows, and then
apply digital logic to arrive at the decision regarding whom he should vote for.
(i) Whether the candidate is a current MLA: M = 1 if yes, else 0.
(ii) If M = 1, the level of his performance, expressed by a 2-bit variable:
P1 P0 = 1 1 if EXCELLENT, 0 1 if GOOD and 0 0 if POOR.
(iii) The level of his HONESTY, expressed by a 2-bit variable H1 H0:
H1 H0 = 1 1 if HIGH, 1 0 if MEDIUM and 0 0 if LOW.
(iv) His stature in his party: S = 1 if HIGH level, else 0.
Based on these pieces of information, he would like to assign a grade to each candidate
on a scale of 0 to 3, represented by a 2-bit variable A1 A0, given on the following basis:
(a) High-level sitting MLA having EXCELLENT performance and HIGH honesty – 11,
(b) Sitting MLA, either having at least GOOD performance and HIGH honesty, or having
EXCELLENT performance and at least MEDIUM honesty – 10,
(c) New candidate having HIGH stature in his party, and a reputation for honesty – 10,
(d) Sitting MLA, having at least GOOD performance and at least MEDIUM honesty – 01,
(e) New candidate who is relatively unknown but has a reputation for honesty – 01,
(f) Sitting MLA, having a record of POOR performance – 00.
Obtain Boolean expressions for the grade variables A1 and A0 in terms of the input
variables M, P1, P0, H1, H0 and S.
Answer
A1 = M•S•P1•(P0)•H1•H0 + M•(P0•H1•H0 + P1•H1) + M’•S•H1•H0,
A0 = M•S•P1•(P0)•H1•H0 + M•P0•H1 + M’•S’•H1•H0.
Most Common Mistake
A large number of students wrote down Boolean expressions
for A1 A0, just listing the six options for grading given in
the question. Separate Boolean expressions for A1 and A0 were
required in the question.
