# Digital Logic T...

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• ###### Question 1
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Consider a quadratic equation x2 – 13x + 36 = 0 with coefficients in a base b. The solutions of this equation in the same base b are x = 5 and x = 6. Then b = _______.

• ###### Question 2
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A function (A, B, C) defined by three boolean variables A, B, and C when expressed as the sum of products is given by:

F = A̅.B̅.C̅ + A̅.B.C̅ + A.B̅.C̅

where, A̅, B̅, and C̅ are the complements of the respective variables. The product of sums (POS) form of the function F is

• ###### Question 3
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What are the first eight bits of mantissa part and the decimal value stored in exponent if  (-28.375)10 is represented in single-precision IEEE 754 format?

• ###### Question 4
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In the following truth table, V = 1 if and only if the input is valid.

 Inputs Outputs D0 D1 D2 D3 X0 X1 V 0 0 0 0 x x 0 1 0 0 0 0 0 1 x 1 0 0 0 1 1 x x 1 0 1 0 1 x x x 1 1 1 1

What function does the truth table represent?

• ###### Question 5
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The clock frequency of 12 MHz is applied to a cascaded counter of modulus-4 counter, modulus-5 counter and modulus-6 counter.

• ###### Question 6
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The simplified Sum of Product form of the following Boolean expression:

$$(P + \bar Q + \bar R )(P + Q+R)(P+Q+\bar R )$$ is

• ###### Question 7
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Consider the unsigned 8-bit point binary number representation below:

X7X6X5X4 .X3X2X1X0

where the position of the binary point is between X4 and X3. X7 is the MSB. Which of the decimal numbers cannot be represented exactly in the above representation:

(a) 14.1875

(b) 16.125

(c)  3.03125

(d) 1.6875

• ###### Question 8
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Consider the function F = A + B̅C, where F is a three-variable Boolean function in which A is MSB and C is LSB. Which of the following is/are false among the given options?

• ###### Question 9
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Consider the 64-bit register which stops floating point number in IEEE Double precision format

What is the value of the number if 64 bits are given below?

 1 10000000111 010111000…

• ###### Question 10
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P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) is

• ###### Question 11
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How many functions does f1.f2 and f1 + f2 represents respectively if the given function is

$${\rm{f}}1{\left( {{\rm{a}},{\rm{b}},{\rm{c}}} \right)_{}} = \mathop \sum \nolimits_M \;\left( {0,{\rm{\;}}1,{\rm{\;}}4} \right) + {\rm{\;}}\mathop \sum \limits_\emptyset \left( {3,{\rm{\;}}5,{\rm{\;}}7} \right)$$

$${\rm{f}}2\left( {{\rm{a}},{\rm{b}},{\rm{c}}} \right) = \mathop \sum \nolimits_M \;\left( {2,3} \right) + {\rm{\;}}\mathop \sum \limits_\emptyset \left( {1,{\rm{\;}}6,{\rm{\;}}7} \right)$$

where ∑m represents sum of min-terms and ∑ϕ represents and don’t care

• ###### Question 12
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D input of a clocked D-flip-flop receives and input A ⊕ Qn where A is an external logic input and Qn is the output of the nth D-FF before the clock appears. The circuit works as

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