ELE 250: MIDTERM EXAM I – Fall 2016
Name:________________________________
ID#:__________________________
Show all of your work. If you do not show your work, you risk not getting any credit for the
problem. Clearly defend all of your conclusions and include any assumptions that are necessary.
Return all parts of this exam.
(Attachments must be handed in with the examination questions)
1. Circle the right Answer for the following questions (2 points each)
1) Which one of the following is not a valid rule for Boolean algebra
a) A+1 = 1
b) A = A’
c) AA = A
d) A+0 = A
2) According to DeMorgan’s Theorms, the following equality (s) are correct:
a) (AB)’ = A’ + B’ b) (XYZ)’ = X’+Y’+Z’
c) (A+B+C)’ = A’B’C’
of these
d) All
3) Determine the values of A, B, C, and D that make the sum term A’+B’+C+D equal to
zero.
a.
A = 1, B = 0, C = 0, D = 0
b.
A = 1, B = 0, C = 1, D = 0
c.
A = 1, B = 1, C = 0, D = 0
d.
A = 1, B = 0, C = 1, D = 1
4) Derive the Boolean expression for the logic circuit shown below:
a.
b.
c.
d.
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5) From the truth table below, determine the Canonical Sum Of Products expression.
a.
b.
c.
d.
6) A five variable K-map has
a)
7)
Sixteen cells b) Thirty two cells
In a 4-variable K-map, a 2-variable product term is produced by
a) A 2 cell group of 1s
cell group of 0s
8)
c) Sixty four cells d) 5 cells
b) an 8 cell group of 1s
c) a 4-cell group of 1s d) A 4
On a K-map, grouping the 0s produces
a) A product of sums expression
b) a sum of products expression
c) a “don’t care” condition
d) AND-OR Logic
9) A 3-input NOR gate has eight input possibilities, how many of those possibilities will result
in a HIGH output?
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a) 1
b) 2
c) 7
d) 8
10) An AND gate with schematic "bubbles" on its inputs performs the same function as
a(n)________ gate
a) NOT b) OR c) NOR d)NAND
2. Answer the following questions (5 points each)
a. Convert the number 1026 to Binary and then convert it from Binary to Hexadecimal and
Octal.
b.
Represent -1026 as a 16-bit signed twos compliment binary representation. Convert this
representation to Hexadecimal and Octal.
c. Determine the base of the numbers having the relationship below for the following operators
to be correct
128/2 = 74
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d. Perform the indicated subtraction with the following signed binary numbers by taking the
2’s complement of the subtrahend. Verify your answers by converting the numbers to their
decimal equivalents performing the operations (Show all work!)
i. 101001-101
ii. 101001-0101
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3. a. Given the function F(A,B,C,D) = ∑m(0,1,2,3,5,7,9,11,13,15). Identify all prime implicants
(number each prime implicant and write down its corresponding product term). Of these,
identify which ones are essential primes. Finally write down the simplified function. (10
points)
b. Using DeMorgan’s Theorem, express the following function
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F = AB’C+A’C’+AB
i.
With only OR and Compliment Operations
(5 points)
ii.
With only AND and Complement Operations (5 points)
4. For the Boolean Functions E and F given in the following Truth Table
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X
Y
Z
E
F
E+F
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
X
0
1
1
0
X
0
1
1
1
0
1
Min terms
E.F
Max Terms
a. Fill in the table above for min terms and Max terms
E’
F’
(2.5 points)
b. Express the functions E and F as a
points)
i.
Sum of minterms (Canonical sum of products)
ii.
Products of Max terms expressions (Canonical product of sums).
(2.5
c. Express the functions E’ and F’ as the
points)
(2.5
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i. Sum of minterms (Canonical sum of products)
ii. Products of Max terms expressions (Canonical product of sums).
d. Express the functions E+F and E.F as the
i. Sum of minterms (Canonical sum of products)
ii. Products of Max terms expressions (Canonical product of sums).
(2.5 points)
e. Simplify E and F to expression with a minimum number of literals using Boolean
Identities or K-map approach (10 points)
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5. Design the simplest combinational circuit with three inputs (A, B and C) and a single
output (F) that would have an out of F= 1 whenever there are more 1s than 0s in the
inputs.
Show the truth table (10 points)
Simply the function using K-maps (10 points)
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