Homework 5 | Complete Solution

Question 1 

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

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Question 2 

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

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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

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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

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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? 

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Question 6 

The waveforms are correct for the logic circuit shown above.
 

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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.

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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:

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Question 9 

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

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Question 10 

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

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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.

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Question 12 

                                        Table 4-1

The truth table in Table 4-1 indicates that:

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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):

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Question 14 

                                     Table 4-1

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

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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?

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Question 16 

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

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Question 17 

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

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Question 18 

Simplifying logic circuits results in:

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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:

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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:

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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:

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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:

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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 :

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