Combinational Logic Circuits

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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Name_________________________ Date____________

Figure 5-4

1) The reason that NOR logic POS networks are redrawn, as in Figure 5-4, is:

A) to minimize the number of parts required

B) to make it easier to determine the logical output

C) that it shows the actual gate arrangement

D) to help make the transition to a K-map

Figure 5-5

2) Figure 5-5: Which figure above represents typical AND-OR logic implementation?

A) Figure A B) Figure B C) Figure C D) Figure D

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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Figure 5-6

3) Which of the choices in Figure 5-6 is equivalent to the Reference Circuit above?

A) Figure (A) B) Figure (B) C) Figure (C) D) Figure (D)

Figure 5-7

4) Figure 5-7: Which of these choices is equivalent to the Reference Circuit?

A) Figure A B) Figure B C) Figure C D) Figure D

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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Refer to the figure below to answer the following question(s).

Figure 5-8

5) Which of the following logic expressions represents the logic diagram in Figure 5-8?

A) 𝑿 = 𝑨 ∙ 𝑩̅̅̅̅ + �̅� ∙ 𝑩 B) 𝑿 = 𝑨 ∙ 𝑩 + 𝑨 ∙ 𝑩

C) 𝑿 = 𝑨 ∙ 𝑩̅̅ ̅̅ ̅̅ + �̅� ∙ �̅� D) 𝑿 = �̅� ∙ �̅� + 𝑨 ∙ 𝑩

6) What type of logic circuit is represented by Figure 5-8?

A) XOR B) XNOR C) XAND D) XNAND

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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Refer to the figure below to answer the following question(s).

Figure 5-9

7) A correct logic expression for Figure 5-9 is:

A) 𝑿 = �̅�𝑩𝑪 + 𝑨�̅�𝑫 B) 𝑿 = (�̅�𝑩)(𝑨�̅�𝑪𝑫) C) (�̅�𝑩)(𝑨𝑪 + �̅�𝑫) D) (𝑨𝑩�̅�)(�̅�𝑩𝑫)

8) The simplest output equation for Figure 5-9 is:

A) 𝑿 = �̅�𝑩�̅�𝑫 B) 𝑿 = �̅�(𝑩�̅� + 𝑪𝑫) C) 𝑿 = 𝑨�̅�𝑪 + 𝑩�̅�𝑫 D) 𝑿 = �̅�(𝑩𝑪𝑫)

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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Questions 9 and 10 relate to the equation: 𝑿 = 𝑨𝑪�̅� + �̅�𝑩(𝑪𝑫 + 𝑩𝑪)

9) How many gates, including inverters, are required to implement the equation before

simplification? Draw out your implementation. You may use gates with MORE than one input!

Answer for # 9 A) 5 B) 9 C) 7 D) 3

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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10) How many gates, including inverters, are required to implement the equation, after

simplification with Boolean algebra? Write out your derivation of the equation and draw your

implementation. You may use gates with MORE than one input!

Answer for #10 A) 5 B) 9 C) 7 D) 3

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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11) The NAND gate is referred to as a "universal" gate, because it:

A) can be found in almost all digital circuits

B) can be used to build all the other types of gates

C) is grown in all the counties of NC

D) was the first gate to be integrated

Figure 5-10

12) Which of the circuits in Figure 5-10 is the sum-of-products implementation of the Reference

Circuit?

A) Figure(A) B) Figure (B) C) Figure (C) D) Figure (D)

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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Refer to the figure below to answer the following question(s).

Figure 5-11

13) Which of the figures in Figure 5-11 represents the NAND implementation of a NOR gate?

A) Figure A B) Figure B C) Figure C D) Figure D

14) Which of the figures in Figure 5-11 represents the NAND implementation of an OR gate?

A) Figure (A) B) Figure (B) C) Figure (C) D) Figure (D)

15) Which of the figures in Figure 5 -11 represents the NAND implementation of an INVERTER gate?

A) Figure (A) B) Figure (B) C) Figure (C) D) Figure (D)

16) The relationship between a NAND gate and a negative-OR gate is expressed by:

A) 𝑨𝑩̅̅ ̅̅ = �̅� + �̅� B) �̅� + �̅� = 𝑨 + 𝑩̅̅ ̅̅ ̅̅ ̅̅ C) 𝑨𝑩 = 𝑨 + 𝑩̅̅ ̅̅ ̅̅ ̅̅ D) 𝑨𝑩 = �̿� + �̿�

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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Figure 5-12

17) The logical equivalent of the Reference Circuit in Figure 5-12 is:

A) Figure (A) B) Figure (B) C) Figure (C) D) Figure (D)

18) When the inverted output of one gate is connected to the inverted input of another gate:

A) the inversions cancel B) a double inversion occurs and the signal is inverted

C) one inversion cancels the other and only a single inversion results

D) All of the above are correct.

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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19) Why are multiple NAND gates used to replace other single function gates?

A) It is easier to design logic circuits with a single gate type, since you only have to fully

understand how one type of gate works.

B) NAND gates are cheaper than any other type of gate.

C) NAND gates are packaged more densely on IC's than other types of gates.

D) It makes it possible to use spare portions of NAND IC packages to implement other logic

functions, perhaps reducing the total IC package count.

Figure 5-13

20) Which of the figures in Figure 5-13 is the correct NAND logic implementation of the expression

𝑿 = 𝑨𝑩𝑪 + �̅�𝑬?

A) Figure (A) B) Figure (B) C) Figure (C) D) Figure (D)

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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21) The relationship between a NOR gate and a negative-AND gate is expressed by:

A) 𝑨 + 𝑩̅̅ ̅̅ ̅̅ ̅̅ = �̅��̅� B) �̅� + �̅� = 𝑨 + 𝑩̅̅ ̅̅ ̅̅ ̅̅ C) 𝑨𝑩 = 𝑨 + 𝑩̅̅ ̅̅ ̅̅ ̅̅ D) 𝑨𝑩 = �̿� + �̿�

Refer to the figure below to answer the following question(s).

Figure 5-14

22) Which of the figures in Figure 5-14 represents the NOR implementation of an OR gate?

A) Figure (A) B) Figure (B) C) Figure (C) D) Figure (D)

23) Which of the figures in Figure 5-14 represents the NOR implementation of an AND gate?

A) Figure (A) B) Figure (B) C) Figure (C) D) Figure(D)

24) Which of the figures in Figure 5-14 represents the NOR implementation of a NAND gate?

A) Figure (A) B) Figure (B) C) Figure (C) D) Figure (D)

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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Figure 5-15

25) The reason that NOR logic networks are redrawn, as shown in Figure 5-15, is:

A) to minimize the number of parts required

B) to make it easier to determine the logical output

C) that it shows the actual gate arrangement

D) to help make the transition to a K-map

Figure 5-16

26) Which of the waveforms shows the correct output for the circuit in Figure 5-16?

A) Ou tput (A) B) Output (B) C) Output (C) D) Output (D)

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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Figure 5-17

27) The point identified as X in Figure 5-17 is referred to as:

A) a node B) a reference point C) a tie point D) common

28) What is the indication of an open in the TTL output of a driving gate?

A) Only the output of the defective gate is affected.

B) The open output reflects back on the input of the driving gate.

C) The connected loads will float to the LOW state.

D) The connected loads will float to the HIGH state.

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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29) What is the indication of a short to ground in the output of a driving gate?

A) Only the output of the defective gate is affected.

B) There is an open circuit to all load gates.

C) The node is stuck in the LOW state.

D) The affected node will be stuck in the HIGH state.

30) What is the indication of a short to ground on the input of a load gate?

A) Only the output of the defective gate is affected.

B) There is a signal loss to all gates connected to that node.

C) The affected node will be stuck in the LOW state.

D) Both B and C are correct.

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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Design Problems

31) Design the logic to control the record function on a VCR. The VCR is to go into record mode if

the record and play buttons on the VCR are pushed at the same time or if the record button on the remote is pressed. The Input signals are ACTIVE HIGH. For the VCR to be in record mode, the Record Enable signal must be low.

𝑃𝑙𝑎𝑦 𝐼𝑛𝑝𝑢𝑡 −

𝑅𝑒𝑐𝑜𝑟𝑑 𝐼𝑛𝑝𝑢𝑡 − − 𝑅𝑒𝑐𝑜𝑟𝑑 𝐸𝑛𝑎𝑏𝑙𝑒̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅̅ ̅

𝑅𝑒𝑚𝑜𝑡𝑒 𝑅𝑒𝑐 𝐼𝑛𝑝𝑢𝑡 −

32) Design the logic to control the temperature in a green house. The temperature must stay

between 72 degrees and 80 degrees. If the temperature is below 72 degrees, a HIGH signal

turns the Heater On. If the temperature is above 80 degrees, a HIGH signal turns the Cooler

On. There are 2 sensors. One outputs a HIGH if the temperature is below 72 degrees and

one outputs a HIGH if the temperature is above 80 degrees. These sensors are prone to

failure, so the design must be able to detect if both sensors are HIGH at the same time. If that

happens, the circuit must turn off the heater, turn off the cooler, and set an alarm signal

HIGH for maintenance.

𝐵𝑒𝑙𝑜𝑤 72 𝑆𝑒𝑛𝑠𝑜𝑟 −

− 𝐻𝑒𝑎𝑡𝑒𝑟 𝑂𝑛

𝐴𝑏𝑜𝑣𝑒 80 𝑆𝑒𝑛𝑠𝑜𝑟 −

− 𝐶𝑜𝑜𝑙𝑒𝑟 𝑂𝑛

− 𝐴𝑙𝑎𝑟𝑚 𝑂𝑛

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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33) Design the logic to monitor the water level in two tanks, A and B. If the level in one tank is

below a sensor level, a pump is turned on that transfers water from one tank to the other until

the level is above the sensor or the levels in both tanks are below the sensors. There is a

pump for each tank. A high on the sensor indicates that the level is correct. A high on the

pump turns it on. Hint: If Sensor A and Sensor B are both high, neither Pump is on. If

Sensor Tank A goes low, Pump B turns on and water is pumped from Tank B into Tank A. If

Sensor Tank B goes low, Pump A turns on and water is pumped from Tank A into Tank B. If

BOTH Sensors are low, nothing can happen because neither tank has water to spare.

𝑆𝑒𝑛𝑠𝑜𝑟 𝑇𝑎𝑛𝑘 𝐴 −

− 𝑃𝑢𝑚𝑝 𝐴 𝑂𝑛

𝑆𝑒𝑛𝑠𝑜𝑟 𝑇𝑎𝑛𝑘 𝐵 −

− 𝑃𝑢𝑚𝑝 𝐵 𝑂𝑛

ELN-133 Chapter 5 Homework Spring 2015 Combinational Logic

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34) Design the logic to control the motor on a simple remote control car. There are two buttons on the remote control for the motor. If neither button is pressed, the car stops. If the top button is pressed, the car moves forward. If the bottom button is pressed, the car moves backwards. If both buttons are pressed, the car spins. There are two motors in the car and each motor has two inputs F and B. A high on F makes the car go forward. A high on B makes the car go backward.

Top Button Bottom Button F1 B1 F2 B2 State

0 0 0 0 0 0 Stopped

0 1 0 1 0 1 Backward

1 0 1 0 1 0 Forward

1 1 0 1 1 0 Spin

From the Truth table, draw the logic diagram.

Top Button - - F1

- B2

Bottom Button - - B1

- F2