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 ≤ _________

Write a program in 8085 Assembly language to Add two 16-bit unsigned BCD(8-4-2-1 Binary Coded Decimal) number. Assume the two input operands are in BC and DE Register pairs. The result should be placed in the register pair BC. (Higher order register in the register pair contains higher order digits of operand)

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

(a) An asynchronous serial communication controller that uses a start stop scheme for controlling the serial I/O of a system is programmed for a string of length seven bits, one parity bit (odd parity) and one step bit. The transmission rate is 1200 bits/second.
(i) What is the complete bit stream that is transmitted for the string ‘0110101’?
(ii) How many such strings can be transmitted per second?

(b) Consider a CRT display that has a text mode display format of 80 × 25 characters with a 9 × 12 character cell. What is the size of the video buffer RAM for the display to be used in monochrome (1 bit per pixel) graphics mode?

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?

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

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

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

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?

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

Zero has two representations in

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

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 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.

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?

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 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 

(34.4)₈ × (23.4)₈ evaluates to

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

(C012.25)_H – (10111001110.101)_B =

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

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

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

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

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