Homework 5 Complete Solution 1

Question: #1325

Question 1

X = ABC + BCD is in the form of minterms expression.

Question 1 options:

	True
	False

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Question 2

Wich of the following sum of products represents the given truth table?

Question 2 options:

a)	X₁X₂X₃'+X₁'X₂'+X₁'X₃'

b)	X₁X₂+X₁'X₂'+X₁'X₃'

c)	X₁X₂X₃'+X₁'X₂'+X₁'X₂X₃'

d)	None of the above

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Question 3

The minterm expression for the function g(A,B,C) given:

g(A,B,C)=A'B + AB' + AC

Question 3 options:

a)	m(2,3,4,5,7)

m(0,1,6)

c)	m(1,3,5,7)

d)	None of the above

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Question 4

The maxterm expression for the function g(A,B,C) given:

g(A,B,C)=A'B + AB' + AC

Question 4 options:

a)	∏M(2,3,4,5,7)

b)	∏M(0,1,6)

c)	∏M(1,3,5,7)

d)	None of the above

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Question 5

For the function:

f(A,B,C,D) = A'BCD+ A'B + ACD'+ BC

What would be the canonical sum of products expansion?

Question 5 options:

a)	f(A,B,C,D)= A'BC'D'+A'BC'D+A'BCD'+ A'BCD + AB'CD'+ABCD'+ ABCD

b)	f(A,B,C,D)= A'BC'D'+A'BC'D+A'BCD'+ A'BCD + ABC'D'

c)	f(A,B,C,D)= A'BC'D'+C'D+A'BCD'+ A'BCD + ABC'D'+ BC'D+BCD'+ CD

d)	The function is already expressed in canonical form

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Question 6

The waveforms are correct for the logic circuit shown above.

Question 6 options:

	True
	False

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Question 7

For circuit shown, which option gives the equivalent, minimal circuit?

Note, the bubble shown in the input B to the lower AND gate in the option a is equivalent to an inverter.

Question 7 options:

Option a

Option b

Option c

d)	None of the above

Hide hint for Question 7

Derive the expression of the circuit as a sum of products, map into a Karnaugh Map, minimize and apply De Morgans

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Question 8

Using Boolean algebra to simplify the expression Z = AB + A(B + C) + B(B + C), the completed first step would result in the expression:

Question 8 options:

	Z = AB + ABAC + BB + BC
	Z = AB + AB + C + BB + C
	Z = AA + AB + AB + AC + BB + BC
	Z = AB + AB + AC + BB + BC

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Question 9

Using Boolean algebra, the complete simplification of Z = AB + A(B + C) + B(B + C) gives us:

Question 9 options:

	Z = AB + AC + B
	Z = B + AC
	Z = AB = AC = BC
	Z = AB + AC + B + BC

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Question 10

Using Boolean algebra, the expression given for Y = above simplifies to:

Question 10 options:

	Y = BC + A'B'C + AB'C
	Y = BC + B'C
	Y = C
	Y = BC +BC' + A'

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Question 11

The implementation of simplified sum-of-products expressions may be easily implemented into actual logic circuits using all ________ with little or no increase in circuit complexity.

Question 11 options:

	OR gates
	AND gates
	NAND gates
	multiple-input inverters

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Question 12

Table 4-1

The truth table in Table 4-1 indicates that:

Question 12 options:

	The output (Z) is HIGH only when a single input is HIGH.
	The output (Z) is HIGH only when the majority of the inputs are HIGH.
	The output (Z) is HIGH only when the binary input count is an even number greater than zero.
	The output (Z) is HIGH only when the binary input count is an odd number.

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Question 13

Table 4-1

The circuit implementation of the sum-of-products expression for Table 4-1 would require (without minimizing):

Question 13 options:

	Three 3-input OR gates, one 2-input AND gate, and five inverters
	Three 3-input AND gates, two 3-input OR gates, and five inverters
	One 3-input OR gate, two 3-input AND gates, and five inverters
	Three 3-input AND gates, one 3-input OR gate, and three inverters

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Question 14

Table 4-1

Circuit implementation of the simplified expression for Table 4-1 will require (as a minimum):

Question 14 options:

	Two 2-input AND gates, two 2-input OR gates, and two inverters.
	Two 2-input AND gates, one 2-input OR gate, and one inverter.
	One 2-input AND gate, two 2-input OR gates, and two inverters.
	Three 2-input AND gates, two 2-input OR gates, and two inverters.

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Question 15

A logic circuit allows a signal (A) to pass to the output without inversion when either (but not both) of the control signals (B₁ and B₂) are HIGH. Which of the following option is the output expression for this circuit?

Question 15 options:

	Option a)
	Option b)
	Option c)
	Option d)

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Question 16

The logic gates required to implement the logic circuit in the preceding question would be:

Question 16 options:

	an Exclusive NOR gate with inputs B₁ and B₂ whose output is fed, along with input A, to an AND gate.
	an Exclusive NOR gate with inputs B₁ and B₂ whose output is fed, along with input A, to an OR gate.
	an Exclusive OR gate with inputs B₁ and B₂ whose output, is fed along with input A, to an AND gate.
	an Exclusive OR gate with inputs B₁ and B₂ whose output is fed, along with input A, to an OR gate.

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Question 17

Which of the following is the simplest form of the expression Y = ABC[AB + C(BC + AC)]?

Question 17 options:

	Y = ABC + BC
	Y = BC
	Y = AC + BC
	V = ABC

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Question 18

Simplifying logic circuits results in:

Question 18 options:

	fewer potential faults.
	fewer connections.
	fewer gates.
	all of the above

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Question 19

Given F₁ = Σ m(0, 4, 5, 6) and F₂ = Σ m(0, 3, 4, 6, 7) the minterm expression for F₁ + F₂ is:

Question 19 options:

	F₁ + F₂ = Σ m(0, 3, 4, 5, 6, 7)
	F₁ + F₂ = Σ m(0, 6)
	F₁ + F₂ = Σ m(1, 2)
	None of the above

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Question 20

Given F₁ = Π M(0, 4, 5, 6) and F₂ = Π M(0, 4, 7) the maxterm expression for F₁ + F₂ is:

Question 20 options:

	F₁ + F₂ = Π M(0, 4, 5, 6, 7)
	F₁ + F₂ = Π M(1, 2, 3)
	F₁ + F₂ = Π M(0, 4)
	None of the above

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Question 21

A switching circuit has four inputs as shown. A and B represent the first and second bit of a binary number N₁ and C andD represent the first and second bit of binary number N₂. The output is to be 1 only if the product N₁xN₂ is less than or equal to 2. The minterm expansion of F is:

Question 21 options:

	F=∑m(0,1,2)
	F=∑m(0,1,2,3,4)
	F=∑m(0,1,2,3,4,5,6,8,9,12)
	None of the above

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Question 22

A bank vault has three locks with a different key for each lock. Each key is owned by a different person. To open the door, at least two people must insert their keys into the assignated lock. The signals A, B and C are 1 if there is a key inserted into lock 1, 2 or 3 respectively. The equation for the variable Z which is 1 iff the door should open is:

Question 22 options:

	Z=AB + AC + BC
	Z=ABC
	Z=A + B + C
	None of the above

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Question 23

A logic circuit realizing the function f has four inputs A, B, C and D. The three inputs A, B, C are the binary representation of the digits 0 through 7 with A being the most-significant bit. The input D is an odd-parity bit, ie the value of D is such that A, B, C and D allways contain an odd number of 1's. (For example, the digit 1 is represented by ABC = 001 and D = 0 and the digit 3 is represented by ABCD = 0111.) The function f has value 1 if the input digit is a prime number. (A number is prime if it divisible only by itself and 1; 2 is considered to be prime but 0 and 1 are not)

A list of the minterms and don't care minterms of f is :

Question 23 options:

		f = ∑m(4,7,11,14) + d(0,3,5,6,9,10,12,15)
		f = ∑m(2,3,5,7) + d(0,1,4,6,8,9,10,11,12,14,15)
		f = ∑m(2,3,5,7,11,13) + d(0,1,2,4,6,8,9,10,12,14,15)
		None of the above
Hide hint for Question 23

Build the truth table for f(A,B,C,D) following the specifications given above. Observe that some of the rows of the truth table cannot hold realistic parameters and will never occurr and therefore should be assigned as don't care