CSCI280: Computer Organization
Practice Test over Chapter 3 of Null
This is a practice test over digital logic. This test has problems that are similar to some of the problems on the actual test. The actual test will be longer than this test and may have questions over topics that are not covered on this practice test. The purpose of this practice test is to give you an idea of both the types of questions to expect on the actual test and the topics that will be covered on the actual test. The actual test will be open book, open notes.
1Use Boolean algebra to simplify the following digital function to only 3 gates:
A'B'C'D' + AB'C'D' + ABC'D + AB'C'D + ABCD + AB'CD + A'B'CD' + AB'CD'
(A'+A)(B'C'D') + (B+B')(AC'D) + (B+B')(ACD) + (A'+A)(B'CD') Distr prop
1(B'C'D') + 1(AC'D) + 1(ACD) + 1(B'CD')Inverse property
(B'C'D') + (AC'D) + (ACD) + (B'CD')Identity property
(B'C'D') + (B'CD') + (AC'D) + (ACD)Commutative property
(C'+C)(B'D') + (C+C')(AD)Distributive property
1(B'D') + 1(AD)Inverse property
B'D' + ADIdentity property
2.Use a Karnaugh map to simplify the following digital function to only 3 gates:
A'BC'D' + A'BCD' + A'BC'D + A'BCD + ABC'D + ABCD
The green box corresponds to the intersection of the columns where D is 1 and B is 1, so it is the term BD.
The blue box corresponds to the row where A is 0 and B is 1, so it is the term A'B.So the function is A'B + BD.
3.Create the truth table for the following function: A'B'C' + A'BC + AB'C + ABC
Draw the circuit diagram.
Write it as a product of sums.
If possible, simplify it.
Truth Table:Circuit Diagram:
A / B / C / F(A,B,C)0 / 0 / 0 / 1
0 / 0 / 1 / 0
0 / 1 / 0 / 0
0 / 1 / 1 / 1
1 / 0 / 0 / 0
1 / 0 / 1 / 1
1 / 1 / 0 / 0
1 / 1 / 1 / 1
Product of sums (use the zero rows): (A+B+C')(A+B'+C)(A'+B+C)(A'+B'+C)
Simplified: A'B'C' + A'BC + AC
4.A multiplexer has 4 control (select) lines. How many input lines and how many output lines does it have?
24 = 16 input, 1 output (a multiplexer always has one output)
5A decoder has 10 input lines. How many output lines does it have?
210 = 1024 (210 is sufficient)
6.A memory chip has 16 address lines. How many memory cells can be accessed?
216 = 65536 (216 is sufficient)
Use the following truth table for the next four questions
A / B / C / f(A,B,C)0 / 0 / 0 / 0
0 / 0 / 1 / 1
0 / 1 / 0 / 0
0 / 1 / 1 / 1
1 / 0 / 0 / 0
1 / 0 / 1 / 1
1 / 1 / 0 / 0
1 / 1 / 1 / 1
8. Write the function as a sum of products:
A'B'C + A'BC + AB'C + ABC
9. Write the function as a product of sums.
(A+B+C)(A+B'+C)(A'+B+C)(A'+B'+C) (Use the zero rows)
10.Use Boolean algebra to simplify the function.
A'B'C + A'BC + AB'C + ABC
A'C(B' + B) + AC(B' + B)Distributive property
A'C(1) + AC(1)Inverse property
A'C + ACIdentity property
C(A' + A)Distributive property
C(1)Inverse property
CIdentity property
11.Use a Karnaugh map to simplify the function.
This is the column where C=1, so the simplified function is C.
12.Draw the circuit diagram using the sum of products form of the function.
13.Find the truth table for the following circuit (8 rows). Note that the left box is a 1-bit adder, and that the other box is a "D" flip-flop. The adder will be updated almost instantly, but the output from the flip-flop will take a tick of the clock to propagate the value from the input to the output (Q).
Truth Table. Note that Z is Q on the current click of the clock. Q(t+1) is the value of Q on the next tick of the clock (after the signals have propagated through the circuit). The two bold red rows below may seem counter-intuitive. But remember that Q(t+1) is the value of Q on the next tick of the clock.
X / Y / Z / S / Q(t+1)0 / 0 / 0 / 0 / 0
0 / 0 / 1 / 0 / 0
0 / 1 / 0 / 1 / 0
0 / 1 / 1 / 0 / 1
1 / 0 / 0 / 1 / 0
1 / 0 / 1 / 0 / 1
1 / 1 / 0 / 1 / 1
1 / 1 / 1 / 1 / 1
14. Find the truth table for the following circuit (8 rows).
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