COMPUTER TECHNOLOGY 2015/2016 Exercises. Unit 7

Transcription

1 COMPUTER TECHNOLOGY 05/06 Exercises. Unit 7 Test. Identify the function of the figure below: A F ABC+ ABC B F ABC+ AB+ ABC C Neither A nor B are true ) About the circuit of the figure below, tick the true answer: A This is an active-low output DEC x4 and all outputs are zero. B This is a decoder x4 and output signals are D0=0, D=0, D=; D3=0 C This is a DEC x4 and all outputs are

2 3) Identify the circuit of the figure below: A MUX 8x with two control inputs B MUX 8x with four control inputs C Answers A and B are false 4) Tick the function table that correspond to this circuit. A B C

3 5) About the circuit of the figure below, tick the true answer. f (0,0,,,) 0 f (,,0,0,) 0 A B C Answers A and B are false 6) Let us assume that ABC and xyz are the binary representations of numbers n and m in the figure below. Tick the true answer: A if n<4 then m=n+ B Always x=0, y=0, z=0 C Always x=0, y=, z=0 7) About the circuit below, tick the true answer. A If A=0, B=, C=, then X=0, Y=, Z=. B Always X=, Y=, Z= C If A=, B=, C=0, then X=0, Y=, Z=.

4 8) Find the correct implementation of function F( a, b, c) M (0,,4,5,7) E MUX 8x F a b c 0 E DEC 3x F c b a 0 E DEC 3x F a b c A B C 9) Tick the true sentence A The active-low enable MUX 6x contains eight 4-input AND gates. B The active-high enable MUX 6x contains sixteen 6-input AND gates. C COD 8x3 contains three 4-input AND gates 0) Find the false sentence A The code converters can be easily implemented by using encoders and decoders B DEC 3x8 and DMUX 8x can perform the same functionality C 7-segment decoder generates minterms.

5 Problems ) Imagine we want to design a combinational circuit to solve the following logic problem. A football club manager decides at the end of the season if the coach continues on the charge (F=) or not (F=0) depending on several aspects. Note that there are only two teams in this curious championship. If the team wins scoring more than 70 points, the coach goes on. Nevertheless, if the team wins but with less than 70 points, the coach will have the same fate than the one of the opponent coach. In case the team reaches 70 points without being the winner, the coach will have the contrary fate than the one of the opponent coach. Finally, when the team loses the championship scoring less than 70 points, the coach is fired. a) Define the inputs and outputs of the problem. b) Find the truth table c) Make an implementation of the logic circuit by using NOR gates In order to take a more collective decision, the manager achieves an agreement with the management board. They conclude that: if the team wins, the same earlier criteria are adopted, otherwise, the decision will be the one of the management board. d) Find the new truth table. e) Make an implementation of the logic circuit by using a MUX 4x. Choose the control inputs as you wish.

6 ) The figure below illustrates an irrigation system of two plots of land (X and Y). The system is composed of a windmill, an engine M, two water tanks controlled by their corresponding valves V X and V y. Note that the volume of tank X is twice the one of tank Y. Besides, tank A has got two level sensors A and B, whereas C has only one level sensor C (the location of sensors A, B and C can be seen in the figure). Finally, the wind sensor S is activated (S=0, active-low signal) when the wind speed is less than 0m/seg. The motor starts up when wind speed is less than 0m/seg and both tanks are not empty. Plot X is irrigated as soon as the tank is full and the wind speed is less than 0m/seg or if S= and the tank is half full. Plot Y is irrigated if and only if there is enough wind-speed and the water level reaches sensor B. a) - Identify input and output variables and set the don t care conditions. - Find the truth table of the problem. b) (.5 puntos) - Implement function M with only one MUX 4x and the necessary NAND gates. - Implement function V X with a DEC x4 network. - Implement V Y with DEC x4, MUX 4x and the necessary gates.

7 3) Figure represents a district with three car-parks (A, B and C) and six traffic lights with two lights each (red and green). As it can be seen in Figure, all streets are one way streets. The goal is to design a combinational circuit that somehow helps a supervisor to control the traffic lights. The supervisor manages the traffic lights through a keyboard composed of seven buttons numbered from 0 to 7. Each time a button is pushed, a specific path between two car-parks is established as follows: - Button opens the path from A to B - Button 3 opens the path from A to C - Button 4 opens the path from B to A - Button opens the path from B to C - Button 6 opens the path from C to A - Button 7 opens the path from C to B - Button 5 closes the traffic in the whole district. All traffic lights are red. - Button 0 disables the system. All traffic lights are OFF. Figure Figure a) Set the inputs and outputs of this combinational circuit. Find the corresponding truth table. b) Implement functions V and V (green lights) with one MUX 4x each. Take two MSB variables as control inputs for V and two LSB variables for V. c) Implement both functions V3 and V4 with only one active-low output DEC3x8 and the necessary gates. d) Implement function R5 (red light) using NAND gates. e) Implement function R6 using NOR gates.

8 4) A Court of Justice is composed of four members, the President (P), the Secretary (S), the Vocal (V) and Vocal (V). To make decisions the court has agreed in the following criteria: If the president absolves the accused, there are two options. First, if any other court member absolves, the accused is eventually acquitted. Second, if the rest of members vote guilty, the accused will be guilty. If the president's vote is 'guilty', the following occurs: If both vocal members plead him innocent, the verdict will be the one of the Secretary. If the votes of both vocal members are different, the verdict will be the one of the Secretary provided the Secretary and President agree, otherwise the accused will be not guilty. In the case both vocal members plead him guilty, the defendant will be guilty. The lawyer appeals (R) to a higher Court of Justice as long as there are at least two positive votes (acquittal) or when the President acquits the defendant. a) Identify inputs and outputs in this logical problem. Find the truth table and set the don t care conditions. Take the following encoding: 0=Innocent, =Guilty. b) Implement function V (verdict) with a MUX 4x and the necessary gates. Take V and V as control inputs. c) Implement the output function V (verdict) with a DEC 4x network (two level tree structure) d) Implement function R with NOR gates.

9 5) Analyze the circuit below and find the truth table. Calculate an equivalent circuit in which outputs A, B C and D are implemented as follows: - A must be implemented with a MUX 8x. Consider input d as MSB - B must be implemented with an active-low output DEC - C must be implemented with a MUX 4x, taking variables LSB as control inputs. - D must be implemented with an active-high output DEC

10 6) Design a combinational circuit that controls the following irrigation system. See figure. The system is composed of: two humidity sensors (A and B) inserted into the plot of land, two level sensors (C and D) located in a water tank, an hydraulic pump (W) which pumps water from a well and three sprinklers (X, Y and Z). The system works as follows - In general, sprinkler X activates when sensor A does not detect humidity (A=0); sprinkler Y starts up when sensor A or B or (A and B) do not detect humidity; sprinkler Z activates when sensor B does not detect humidity (B=0). - If the water tank is empty (C=0 y D=0), none of the sprinklers is activated with two exceptions: ) when only sensor A does not detect humidity, only X is activated, ) when only sensor B does not detect humidity, only sprinkler Z is activated. - Hydraulic pump (W) starts up if: a) The water tank is empty (C=0 y D=0) with the exception of that both sensors A and B detect humidity. b) The water tank is half full (C= y D=0) and both sensors A and B do not detect humidity. - Hydraulic pump (W) never is activated if the water tank is full (C= y D=). Consider that in the rest of cases W=0. a) Identify inputs, outputs and don t care conditions of the problem. Find the truth table. b) Implement X with a active-low output DEC 3x8. Find firstly the expression of W. c) Implement Y with a MUX 8x. d) Implement Z with two MUX 4x e) Implement W by means of a decoder and multiplexer network (two level tree structure)