EE 2310 HW #4

The complement of the expression, Y = A*B + C + D

(A + B')*C'*D' my choice

Use Shannons expansion to reduce the following boolean expression, ( a + b + d)*(a' + b + c)*(b + c + d + e + f)

(a + b + d)*(a '+ b + c) my choice

Convert (-29) to binary and (-43) to binary and add them

-(01001000)2 my choice

Given a 3-bit input denoting day of week (000 = Sunday,001 = Monday, ..., 110 = Saturday), construct a truth table in terms of F(a,b,c) and circuit to say if a given day is a weekend (1 if weekday, 0 otherwise). How many gates and of what logic would be required. (Note - Consider that 1,1,1 will be don't care and use kmaps to obtain the logic )

. 1 XNOR, 1 OR b. 1 XOR and 1 AND wrong c. 1 XOR and 1 OR d. 1 XNOR and 1 AND my choice

For the given circuit below, find the output y when a = 1, b =0 and c =1.

. 1 my choice

Which of the following is an invalid BCD code.

. 1110 my choice

From the Kmap given below reduce the boolean expression in SOP form, a*ba*ba*babc*d0 110c*d10 0 1c*d1 0 0 1 c*d01 1 0

. B*D' + B'*D b. (B + D)*(B' + D') my choice c. (B' + D)*(B + D') wrong d. (B + D + C')*(B' + C +D') wrong e. None

Simplify the following expression, F = X'*Y'*Z + X'*Y*Z + X*Y'*Z + X*Y*Z

. F = X*Z' + X*Z b. F = Y'*Z'*X + Y*X'*Z c. Z d. None e. F = Y*Z' + X*Z my choice

For the truth table given below, write the POS form,

. O = (A + B + C')*(A' + B' + C)*(A '+ B' + C') my choice

Reduce the following using consensus theorem Y = (D + F) * (E + F) * (D + E)

. Y = (D' + F) * (E' + F') my choice

Simplify the following boolean equation, (X'+ W*Y + Z')*(X' + W*Y + Z)

. a. X' + W*Y my choice b. Z*W + Y c. W' + Y'*Z' d. None e. X*W' + Z m choice #2

Use Shannons expansion to reduce the following boolean expression, x*y*z + x*y + z*y (Note = start with x)

. x b. None c. x' wrong d. y e. z

Convert (11100)2 to it's 8421 BCD equivalent.

00101000 my chice

What is the 1's complement of 5010. Represent the answer in binary.

001101 my choice

Subtract (C9)16 and (C)16 and represent the answer in binary

010111101 my choice

Obtain the minterms for the function (F). Reduce F using kmaps. How many NAND gates would you require to synthesize the circuit. Assume you have the input logic and its complement available to you. F(A,B,C,D) = A'*B'*C + A*C' + A*C*D +A*C*D' + A'*B''*D'

1 2-input NAND gate(s) and 1 3-input NAND gate(s) b. wrong None c. 1 2-input NAND gate(s) and 2 3-input NAND gate(s)wrong d. 3 2-input NAND gate(s) and 2 3-input NAND gate(s) e. 2 2-input NAND gate(s) and 1 3-input NAND gate(s) my choice

Obtain the boolean expression at Q and consider the following inputs A = 1, B=0, C=0. What would the logic at Q be?

1 my choice

The gray code for decimal number 18 is equivalent to

11011

Consider the following truth table which is for a adder and obtain an equation for Cout with the help of Kmaps. Synthesize the equation.

3 2-input AND and 1 3-input OR gates my choice

Consider the following kmap, the number of essential prime implicants for the question will be ,

3 my answer

How many Nor Gates will be required to synthesis the following kmap

4

A burglar alarm (A) is controlled by a switch (S). When the switch (S) is on, the alarm sounds if either the front(F) or back(B) or both the doors are opened. The alarm will not work if the switch is off. Which of the following boolean represents the above statement. Consider the following variables Alarm - A, Front Door (F), Back Door (B), Switch(S). Make sure you have covered all the cases.

A = S*(F + B) my choice

After complement use DeMorgans Theorem on the following boolean expression, (A + B)*(B + C)*(A + C)

A'*B' + B'*C + A'*C' my choice

Which if the following represents the distributive law.

A(b+c)=AB+AC

Given that m13 is a minterm of A,B,C and D, which of the following represents m13 (NOTE - Consider A as the Most significant Digit and D as the Least Significant Digit)

A*B*C'*D my choice

Which of the following statements about "X" is correct. 2AND2 1OR 2 inveter

A.B.C my choice)

Simplify the following boolean equation, [A*B(C + B*D) + A*B]*C

B'*C my choice

Simplify the following expression, F = X'*Y'*Z + X'*Y*Z + X*Y'*Z + X*Y*Z

F = Y'*Z'*X + Y*X'*Z wrong b. F = Y*Z' + X*Z wrong c. None d. F = X*Z' + X*Z wrong e. Z

From the following table obtain and reduce the logic equation for Y.

None b. B*C' + A'*C + A*C wrong c. B*C + B'*C' my choice d. B*C' + A'*B + A*C wrong e. B*C' + A' + B'

Convert the following expression from POS to SOP form and then deduce the minterms from the SOP equation, Y = (K + L + M)*(K + L' + M)*(K + L '+ M')*(K' + L' + M)*(K' + L' + M')

Y = Σm(1,4,5) my choice

Find a minimum sum of products expresssion for F = a*b*c + b*c*d + c*d + a*b

a*b +c*d + b*c my choice

Convert (B= -66) and (A= -75) to unsigned binary and subtract them (A-B)

a. (00001001)2 wrong b. -(00010101)2 c. None d. -(00001001)2 my choice e. -(11110110)2

From the Kmap given below reduce the boolean expression obtained, (Note - the following kmap is in POS form)

a. (X + Y' )*(W + X' + Z) wrongb. None c. (Z' + X)*(Z + W' + X') my choice d. (Y' + Z)*(W + X + Z') e. (X' + Z)*(W' + X + Z) wrong

Use Shannons expansion to reduce the following boolean expression, (x + y + z)*(x + y + z)*(y + z)

a. (x + y)(x' + z) my choice

The gate level representation of the following transistor implementation,

a. 2-imput NOR b. XOR wrong c. None d. 2-input NAND e. 3-input NOR wrong

Synthesize a circuit with minimum that detects prime numbers from 0 to 7. (Note the prime numbers are 2,3,5,7) (Hint - Use SOP equation and then synthesize the logic equation)

a. 3 Not gate(s), 3 AND gate(s) and 3 OR gate(s) b. 2 Not gate(s), 4 AND gate(s) and 2 OR gate(s) c. 1 Not gate(s), 2 AND gate(s) and 1 OR gate(s) my choice d. 1 Not gate(s), 1 AND gate(s) and 3 OR gate(s)

Convert 489.310 to base 6.

a. 423.666...6wrong b. 420.667...6 c. None of the above d. 423.666....6 e. 425.667...6

How many NOR gates will be required to synthesize the following kmap,

a. 6 b. 5 c. None d. 3 wrong e. 4

Simply the following boolean expression, B*(A + C) + (A + B) + (B*C) + C

a. A + B + C b. A c. A + B + C wrong d. A + B e. None

Consider the following truth table which is for a adder and obtain an equation for Sum with the help of Kmaps

a. A'*B*Cin + Cin*A*B' + A*Cin'*B + A*Cin*B wrong b. A'*B'*Cin + A'*B*Cin' + A'*B*Cin + A*B'*Cin c. A*B'*Cin + A*B'*Cin' + A*B*Cin wrong d. None my answer e. A'*B'*Cin + A'*B*Cin' + A'*B*Cin + A*B*Cin wrong

Convert the equation (in Figure -12) to its min-term form. (It is currently in its max-term form).

a. A*B*C + A*B'*C b. A'*B*C + A*B'*C my choice c. A*B*C' + A*B'*C d. None e. A'*B'*C + A*B*C'

With the help of Kmaps reduce the following minterms, F(A,B,C,D) = Σm(7,8,9) and 6,12,13,14,15 as don't cares.

a. A*C + C*B wrong b. None my choice c. C*B + A*D wrong d. B*A + C*D wrong e. B'*D + A*C wrong

Why is Gray Code more practical to use while coding.

a. Alternate digit change between counts. b. All digits change between counts. c. Two digits change between counts. d. Only one digit changes between counts. my choice e. None of the above.

Consider the following truth table and reduce it with the help of Kmaps abcdo

a. B'*C + A*C*D' + A*C*C' + A'*B*C + A*B*D wrong b. A'*C + A*B'*C + A*B*C' + A'*B*C + A*B*C wrong c. B'*C + A*B'*C + B*C*D' + A'*B*D + A*B*D wrong d. None e. B'*D + B*C'*D' + A*B*C' + A''*B*C + A*B'*C my choice

From the Kmap given below reduce the boolean expression obtained, a'.b'.a.b' a.a a.b'

a. B'*D' + A*C' b. A'*C + A*C' wrong c. A'*C + A*C'*D d. None e. A'*C + A*B

From the Kmap given below reduce the boolean expression obtained,

a. B*D*C + A*D + A*C*D b. B*C*D + A*C + A*C*D c. A'*C*D + A*B + B*C wrong d. None e. A*B'*C' + A'*D'+ C'*D' my choice

Design a Minority Logic Circuit such that there are 3 inputs, output(y) is active when the number of 0's are greater than 1's in the prime implicant.With the help of Kmaps reduce the boolean expression. How many NAND gates will you require to synthesize the reduced boolean equation. (note - to negate logic also use a NAND gate)

a. None b. 2 wrong c. 4 wrong d. 8 e. 6 wrong

Find the maxterms for the given equation, F(a,b,c) = a*b' + b'*c + a*c

a. None b. F(A,B,C,D) = πM(0,2,3,7) wrong c. F(A,B,C,D) = πM(0,1,3,6) my choice d. F(A,B,C,D) = πM(1,2,5,6) e. F(A,B,C,D) = πM(0,1,3,6) wrong

The below given circuit is an example of a multi-output circuit. What would be the expression at O0

a. O0 = I*S0'*S1' my choice b. None c. O0 = I*S0'*S1 d. O0 = I*S0*S1' e. O0 = I'*S0*S1'

The following transistor level circuit is a representation of which of the following gate,

a. OR b. AND wrong c. NOR d. NAND wronge e. None

Which gate has been realized in the transistor circuit below, (NOTE -There are Negations above a few alphabets)

a. OR b. None c. AND d. NAND MY choice e. XOR

Simplify the following boolean equation, X'*W + Y + Z'*(Y + X'*W)

a. X*W' + Z*Y b. None c. X'*W + Y wrong d. Y'*W' + X*Z e. Z*W + Y

From the Kmap given below which of the following can be boolean expression obtained,

a. X*Y + W*Y b. (W + X)*(W' + Y)*(X' + Y) c. (X + W)*Y wrong d. All e. None

From the following table obtain and reduce the logic equation for Y. Which gate will you use to synthesize the logic obtained

a. XNOR b. NAND my choice c. NOR wrong d. None e. XOR wrong

Write a function F(a,b,c) that will detect all the odd numbers from 0 - 7. (Hint - get the truth table, the output of the truth table will be 1 if the decimal equivalent is an even number. The inputs of thr gate are a,b,c where 'a' is the Most Significant Bit (MSB) and 'c' is the Least significant bit(LSB)).

a. b*c wrong b. c' wrong c. c d. None e. b'+c wrong

Which of the following is an example of Idempotent law

a. x*x = x my choice b. x + x = 2x c. x + x' = 0 wrong None e. x*x' = x'

With the help of Kmaps reduce the following minterms, F(x,y,z) = Σm(0,2,4,6)

a. z' my choice b. z c. y' wrong d. x wrong e. None

Obtain the minterms from the following boolean expression,F(A,B,C,D) = A*B*D + A*B*C + A*C*D

a. Σm(4,6,7,9,11,12) wrong b. Σm(4,5,6,14,15) wrong c. None d. Σm(6,7,9,10,11) my choice e. Σm(1,4,13,14,15) wrong

From the Kmap given below reduce the boolean expression obtained and synthesize the boolean expression using NOR gates, (Note : assume that you have to create the complement as well with a NOR gate)

a. 2 my choic #3 b. None c. 3 my choice #2 d. 4 my choice e. 1

Which of the following is the 8-bit binary representation of (-5)10

c. (1111011)2 my choice

Reduce the following function by using Boolean laws: F(A, B, C, D) = (A + C) (A + C) (A + B + C*D)

c. A' my choice

Which property is shown in the following boolean expression, X +(Y*Z) = (X + Y)*(X + Z)

distributive law

Obtain the boolean expression at 'F' for the following logic circuit t4,

x'*y' + x*z + y'*z my choice

Obtain the boolean expression at 'F' for the following logic circuit,

x'*z + x*y + x*z my answer

A bulb in a staircases has two switches, one switch being at the ground floor and the other one at the first floor. The bulb can be turned ON and also can be turned OFF by and one of the switches irrespective of the state of the other switch. The logic of switching of the bulb resembles.

xor gate

Do the following circuits yield the same logic?

yes

Do the following circuits yield the same logic? #2

yes