In 16-bit 2's complement representation, the decimal number -28 is:

Two numbers are chosen independently and uniformly at random from the set {1, 2, ..., 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ______.

Consider Z = X - Y, where X, Y and Z are all in sign-magnitude form. X and Y are each represented in n bits. To avoid overflow, the representation of Z would require a minimum of:

Consider the unsigned 8-bit fixed point binary number representation below,

b₇b₆b₅b₄b₃ ⋅ b₂b₁b₀

where the position of the binary point is between b₃ and b₂ . Assume b₇ is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the above representation:

(i) 31.500    (ii) 0.875    (iii) 12.100    (iv) 3.001

Which one of the following statements is true?

The n-bit fixed-point representation of an unsigned real number X uses f bits for the fraction part. Let i = n-f. The range of decimal values for X in this representation is

The representation of the value of a 16-bit unsigned integer X in hexadecimal number system is BCA9. The representation of the value of X in octal number system is

Given the following binary number in 32-bit (single precision) IEEE-754 format:

The decimal value closest to this floating-point number is

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=________.

Consider a binary code that consists of only four valid code words as given below:

Let the minimum Hamming distance of the code be p and the maximum number of erroneous bits that can be corrected by the code be q. Then the values of p and q are

The 16-bit 2’s complement representation of an integer is 1111 1111 1111 0101; its decimal representation is __________.

Let X be the number of distinct 16-bit integers in 2’s complement representation. Let Y be the number of distinct 16-bit integers in sign magnitude representation.

Then X-Y is _________.

The base (or radix) of the number system such that the following equation holds is_________.

        312/20 = 13.1     

Consider the equation (123)₅ = (x8)_y with x and y as unknown. The number of possible solutions is __________.

The value of a float type variable is represented using the single-precision 32-bit floating point format of IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable X is assigned the decimal value of −14.25. The representation of X in hexadecimal notation is

Consider the following minterm expression for F:

  F(P,Q,R,S) = Σ0,2,5,7,8,10,13,15  

The minterms 2, 7, 8 and 13 are 'do not care' terms. The minimal sum-of-products form for F is:

Let ⊕ 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:

     F(P,Q) = ((1⊕P)⊕(P⊕Q))⊕((P⊕Q)⊕(Q⊕0)) 

The equivalent expression for F is

The smallest integer that can be represented by an 8-bit number in 2’s complement form is

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

The decimal value 0.5 in IEEE single precision floating point representation has

P is a 16-bit signed integer. The 2's complement representation of P is (F87B)₁₆. The 2's complement representation of 8*P is

(1217)₈ is equivalent to

In the IEEE floating point representation, the hexadecimal value 0×00000000 corresponds to

Let r denote number system radix. The only value(s) of r that satisfy the equation is/are

Consider numbers represented in 4-bit gray code. Let h₃h₂h₁h₀ be the gray code representation of a number n and let g₃g₂g₁g₀ be the gray code of (n+1)(modulo 16) value of the number. Which one of the following functions is correct?

The range of integers that can be represented by an n bit 2's complement number system is:

The hexadecimal representation of 657₈ is

Consider the following floating point format.

Mantissa is a pure fraction in sign-magnitude form.

The decimal number 0.239 × 2¹³ has the following hexadecimal representation (without normalization and rounding off:

Consider the following floating point format.

Mantissa is a pure fraction in sign-magnitude form.

The normalized representation for the above format is specified as follows. The mantissa has an implicit 1 preceding the binary (radix) point. Assume that only 0's are padded in while shifting a field. The normalized representation of the above number (0.239 × 2¹³) is

If 73_x (in base-x number system) is equal to 54_y (in base-y number system), the possible values of x and y are

What is the result of evaluating the following two expressions using three-digit floating point arithmetic with rounding?

   (113. + -111.) + 7.51
   113. + (-111. + 7.51) 

Let A = 1111 1010 and B = 0000 1010 be two 8-bit 2's complement numbers. Their product in 2's complement is

Assuming all numbers are in 2's complement representation, which of the following numbers is divisible by 11111011?

The following is a scheme for floating point number representation using 16 bits.

Let s, e, and m be the numbers represented in binary in the sign, exponent, and mantissa fields respectively. Then the floating point number represented is:

What is the maximum difference between two successive real numbers representable in this system?

The decimal value 0.25

The 2’s complement representation of the decimal value -15 is

Sign extension is a step in

In 2’s complement addition, overflow

Consider the following 32-bit floating-point representation scheme as shown in the formal below. A value is specified by 3 fields, a one bit sign field (with 0 for positive and 1 for negative values), a 24 bit fraction field (with the binary point being at the left end of the fraction bits), and a 7 bit exponent field (in excess-64 signed integer representation, with 16 being the base of exponentiation). The sign bit is the most significant bit.

(a) It is required to represent the decimal value –7.5 as a normalized floating point number in the given format. Derive the values of the various fields. Express your final answer in the hexadecimal.

(b) What is the largest values that can be represented using this format? Express your answer as the nearest power of 10.

The 2’s complement representation of (-539)₁₀ in hexadecimal is

Consider the circuit shown below. The output of a 2:1 Mux is given by the function (ac' + bc).

Which of the following is true?

The number 43 in 2’s complement representation is

Consider the values A = 2.0 x 10³⁰, B = -2.0 x 10³⁰, C = 1.0, and the sequence

             X: = A + B    Y: = A + C
             X: = X + C    Y: = Y + B  

executed on a computer where floating-point numbers are represented with 32 bits. The values for X and Y will be

Booth’s coding in 8 bits for the decimal number –57 is

Zero has two representations in

The octal representation of an integer is (342)₈. If this were to be treated as an eight-bit integer is an 8085 based computer, its decimal equivalent is

Suppose the domain set of an attribute consists of signed four digit numbers. What is the percentage of reduction in storage space of this attribute if  it is stored as an integer rather than in character form?

Given √224)_r = 13)_r.
The value of the radix r is:

Consider the following floating point number representation

The exponent is in 2's complement representation and mantissa is in the sign magnitude representation. The range of the magnitude of the normalized numbers in this representation is

The number of 1’s in the binary representation of
(3*4096 + 15*256 + 5*16 + 3) are:

Consider n-bit (including sign bit) 2’s complement representation of integer number. The range of integer values, N, that can be represented is _________ ≤ N ≤ _________

Consider three registers R1, R2 and R3 that store numbers in IEEE-754 single precision floating point format. Assume that R1 and R2 contain the values (in hexadecimal notation) 0x42200000 and 0xC1200000, respectively.

If R3 = R1/R2, what is the value stored in R3?

Convert the following numbers in the given bases into their equivalents in the desired bases.
(a) 110.101)₂ = x)₁₀
(b) 1118)₁₀ = y)_H

Consider the number given by the decimal expression:

  163 * 9 + 162 * 7 + 16 * 5 + 3

The number of 1’s in the unsigned binary representation of the number is ________.

When two 4-bit binary number A = a₃a₂a₁a₀ and B = b₃b₂b₁b₀ are multiplied, the digit c₁ of the product C is given by _________

The exponent of a floating-point number is represented in excess-N code so that:

The following bit pattern represents a floating point number in IEEE 754 single precision format

 110000011101000000000000000000000

A processor that has carry, overflow and sign flag bits as part of its program status word (PSW) performs addition of the following two 2's complement numbers 01001101 and 11101001. After the execution of this addition operation, the status of the carry, overflow and sign flags, respectively will be:

The two numbers given below are multiplied using the Booth's algorithm.

Multiplicand : 0101 1010 1110 1110 
Multiplier: 0111 0111 1011 1101

(C012.25)_H – (10111001110.101)_B =

The addition of 4-bit, two’s complement, binary numbers 1101 and 0100 results in

When multiplicand Y is multiplied by multiplier X = x_n-1x_n-2 ...x₀ using bit-pair recoding in Booth's algorithm, partial products are generated according to the following table.

The partial products for rows 5 and 8 are

(34.4)₈ × (23.4)₈ evaluates to

The number (123456)₈ is equivalent to

Consider a parity check code with three data bits and four parity check bits. Three of the code words are 0101011, 1001101 and 1110001. Which of the following are also code words?

1. 0010111             
2. 0110110         
3. 1011010             
4. 0111010 

To guarantee correction of upto t errors, the minimum Hamming distance dmin in a block code must be

The hexadecimal equivalent of the binary integer number 110101101 is :

In computers, subtraction is generally carried out by

Suppose x and y are floating point variables that have been assigned the values x = 8.8 and y = 3.5. What will be the value of the following arithmetic expression?

2 * x / 3 * y

What is the base(radix) of the number system whose numbers 312, 20 and 13.1 satisfy the following equation?

What is the hexadecimal representation of the decimal number 8537?

Which of the following is a recursive algorithm to convert a positive decimal integers into equivalent binary integers?

The signed 2’s complement representation of -33 is:

Using signed 2’s complement subtraction the result of 11111010-11110011 is: