Digital Systems: From Logic Gates to Processors Week 3 Quiz Answer

Digital Systems: From Logic Gates to Processors Week 3 Quiz Answer

In this article i am gone to share Coursera Course: Digital Systems: From Logic Gates to Processors Week 3 Quiz Answer with you..

Graded Quiz 3 Answer

Question 1)

In n=4, what set(s) of cube(s) is(are) equivalent to the set {0001, 0011, 0100, 0101, 1010, 1011, 1100, 1110}? (equivalent= they cover the same set of minterms)

00x1, 010x, x1x0, 101x
00x1, 010x, 11x0, 101x
x100, 0x01, x011, 1x10
x100, 0x0x, x011, 1x10

Question 2)

Design a circuit to compare two 2-bit numbers A and B (A = a1 a0; B = b1 b0). The circuit has three outputs G (greater than), E (equal to) and L (less than) so that:

G = 1 if A > B,

E = 1 if A = B, and

L = 1 if A < B.

Note: Inputs to the circuit must be named as a1, a0, b1, b0, G, E and L. Respect upper and lower cases.

Instructions to answer this question

1) In the virtual machine, open VerilUOC_Desktop and draw the circuit.

2) Click in “Simulate”->”Verification” and then click in the VerilCirc tab.

3) In "Module" select "Graded Exercises" and click on exercise 3.2.a.

4) VerilCirc returns a 4 uppercase letters code. Type it in the answer box.

Answer: YTZE

Question 3)

Design a digital circuit that receives a 4 bits BCD-coded(*) number X = abcd and returns a signal M5=1 if X=0 or multiple of 5; and M5=0 otherwise. The algorithm below shows the functional description of the circuit ("dc" means a “don’t care” combination).

Inputs and outputs of the circuit must be named as: a, b, c, d, and M5. Respect the upper and lowercases.

(*): BCD code (Binary Coded Decimal) encodes any base-10 number from 0 to 9 in base-2, using 4 bits. That is, 0 is coded by 0000, 1 by 0001, 2 by 0010 and so on until 9, which is encoded by 1001. Base-10 numbers higher than 9 require at least 2 digits and, consequently, they will never enter to the circuit.

if X > 1001 then M5<=dc;

elsif (X=0000 or X=0101) then M5<=1;

else M5<=0;

end if;

Instructions to answer this question

1) In the virtual machine, open VerilUOC_Desktop and draw the circuit.

2) Click in “Simulate”->”Verification” and then click in the VerilCirc tab.

3) In "Module" select "Graded Exercises" and click on exercise 3.3.b.

4) VerilCirc returns a 4 uppercase letters code. Type it in the answer box.

Answer: OWKC

Question 4)

A water tank A receives inputs from two wells (Well 1, Well 2). Each well has a level sensor that generates a signal n1=1 (or n2=1) when the water level is above a threshold, and a tab allowing the water flow into tank A when K1=1 (or K2=1). The level sensor of tank A generates two signals nA1 and nA2, which meaning is explained in the table below. Tank A can be emptied by opening KA (KA=1 opens the flow of water).

We want to design a circuit to control the opening and closing of the keys K1, K2 and KA so that the tank level is maintained in the value "Appropriate" whenever possible. If the level of well 1 or well 2 is low (n1=0 or n2=0), water cannot be drawn from it to fill the tank (tab must be closed). When the level of well A is not "Appropriate", tabs K1, K2, KA must be opened or closed so that A recovers the "Appropriate" level as soon as possible.

(Note: Inputs and outputs of the circuit must be named as: n1, n2, nA1, nA2, K1, K2 and KA. Respect the upper and lower case)

Instructions to answer this question

1) In the virtual machine, open VerilUOC_Desktop and draw the circuit.

2) Click in “Simulate”->”Verification” and then click in the VerilCirc tab.

3) In "Module" select "Graded Exercises" and click on exercise 3.4.b.

4) VerilCirc returns a 4 uppercase letters code. Type it in the answer box.

Answer:

Question 5)

The following circuit consists of 7 identical components with 2 inputs "a" and "b", and 2 outputs "c" and "d". The maximum propagation time from inputs "a" or "b" to outputs "c" or"d" is equal to 0.5 ns. Which is the maximum propagation time from any input to any output (in ns.)?

Introduce the answer in nanoseconds, with 1 decimal digit. Examples: If the propagation time is 8.9 ns., introduce 8.9; if the propagation time is 6 ns., introduce 6.0

Answer: 2.5

Question 6)

Answer:

Question 7)

(This exercise and the next one refer to the same statement)

Consider a system with three input signals x, y and max and one output signal z. All signals are binary encoded non-negative integers.

System specification:

if (x - y) belongs to the interval 0 ≤ x - y ≤ max, then z = x - y;

if (x - y) > max, then z = max;

if (x - y) < 0, then z = 0.

Assume that a procedure difference(A, B, s, C) has been previously defined, where A, B and C are non-negative integers and s is a 1-bit number, so that it computes the difference A – B under the form A – B = (-1)s•C (s is the sign and C is the absolute value of the result).

Which of the following algorithms properly describes the system?

difference(x, y, a, b);
difference(max, b, c, d);
if c = 1 then e <= max; else e <= b; end if;
if a = 1 then z <= 0; else z <= e; end if;

Question 8)

(Let's continue with the last question)

Assume that a module implementing the procedure difference(A, B, s, C) exists. If x and y are 4-bit numbers, which of the following circuits implements the desired system?

Answer: