Digital Logic T...

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 = _______.

Simplify Y = AB’ + (A’ + B)C

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

Find values of Boolean variables A,B,C which satisfy the following equations:

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?

Complement of the expression A’B + CD’ is:

In boolean algebra, the OR operation is performed by which properties?

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

The simplified Sum of Product form of the following Boolean expression:

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

In the circuit shown below, X and Y are digital inputs, and Z is a digital output. The equivalent circuit is a

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

The function AB’C + A’BC + ABC’ + A’B’C + AB’C’ is equivalent to

Which of the following expressions is equivalent to 

If P,Q,R are Boolean variables, then

In boolean algebra, the OR operation is performed by which properties?

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?

Which one of the following expressions does NOT represent exclusive NOR of x and y?

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

denote the exclusive OR (XOR) operation. Let '1' and '0' denote the binary constants. Consider the following Boolean expression for F over two variables P and Q:

The equivalent expression for is

The equivalent expression for F is

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

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

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

D input of a clocked D-flip-flop receives and input A ⊕ Q_n where A is an external logic input and Q_n is the output of the n^th D-FF before the clock appears. The circuit works as