Number Representation

The 32-bit IEEE 754 single precision representation of a number is 0xC2710000. The number in decimal representation is $\_\_\_\_$ . (rounded off to two decimal places)

Consider the real valued variables $X, Y$ and $Z$ represented using the IEEE 754 singleprecision floating-point format. The binary representations of $X$ and $Y$ in hexadecimal notation are as follows: $$ X: 35 C 00000 \...

Consider the 8-bit signed integers $X, Y$ and $Z$ represented using the sign-magnitude form. The binary representations of $X$ and $Y$ are as follows: $$ X: 10110100 \quad Y: 01001100 $$ Which of the following operations...

In a system, numbers are represented using 4-bit two's complement form. Consider four numbers $N 1=1011, N 2=1101, N 3=1010$ and $N 4=1001$ in the system. Which of the following operations will result in arithmetic overf...

The number -6 can be represented as 1010 in 4-bit 2's complement representation. Which of the following is/are CORRECT 2's complement representation(s) of $-6$ ?

The following two signed 2's complement numbers (multiplicand M and multiplier Q ) are being multiplied using Booth's algorithm : M : 1100110111101101 and Q : 1010010010101010 The total number of addition and subtraction...

Three floating point numbers $X, Y$, and $Z$ are stored in three registers $R_X, R_Y$, and $R_Z$, respectively in IEEE 754 single precision format as given below in hexadecimal: $$R_X=0 \times C 1100000, R_Y=0 \times 40...

Consider a system that uses 5 bits for representing signed integers in 2’s complement format. In this system, two integers A and B are represented as A =01010 and B =11010. Which one of the following operations will resu...

The format of a single-precision floating-point number as per the IEEE 754 standard is: Sign (1 bit) Exponent (8 bits) Mantissa (23 bits) Choose the largest floating-point number among the following options.

Which of the following is/are EQUAL to 224 in radix-5 (i.e., base-5) notation?

Consider the IEEE-754 single precision floating point numbers P=0xC1800000 and Q=0x3F5C2EF4. Which one of the following corresponds to the product of these numbers (i.e., P $$\times$$ Q), represented in the IEEE-754 sing...

A particular number is written as 132 in radix-4 representation. The same number in radix-5 representation is ____________.

Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1 + R2, which one of the following values of R1 and R2 gives an arithmetic overflow?

Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127. S: 1 E: 10000001 F : 11110000000000000000000 Here S, E and F denote the sign, exponent and fraction...

Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?

If the numerical value of a 2-byte unsigned integer on a little endian computer is 255 more than that on a big endian computer, which of the following choices represent(s) the unsigned integer on a little endian computer...

The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows: sign exponent mantissa Which one of the following choices is correct with respect to the small...

If x and y are two decimal digits and (0.1101) 2 = (0.8xy5) 10 , the decimal value of x + y is ______

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...

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

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

Consider the equation $${\left( {123} \right)_5} = {\left( {x8} \right)_y}$$ with $$x$$ and $$y$$ as unknown. The number of possible solutions is _________.

Suppose n and p are unsigned int variables in a C program. We wish to set p to $${}^n{C_3}$$. If n is large, which one of the following statements is most likely to set p correctly?

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 mant...

Consider the function func shown below: int func(int num) { int count = 0; while(num) { count++; num >>= 1; } return (count); } The value returned by func(435) is _________.

The base (or radix) of the number system such that the following equation holds is __________ $${{312} \over {20}} = 13.1$$

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

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

Consider the following recursive C function that takes two arguments: unsigned int foo (unsigned int n, unsigned int r) { if (n > 0) return((n % r) + foo(n/r, r)); else return 0; } What is the return value of the functio...

$$P$$ is a $$16$$-bit signed integer. The $$2's$$ complement representtation of $$P$$ is $${\left( {F87B} \right)_{16}}$$ . The $$2's$$ complement representation of $$8{}^ * \,P$$ is

$${\left( {1217} \right)_8}$$ is equivalent to

In the $$IEEE$$ floating point representation the hexadecimal value $$0\, \times \,00000000$$ corresponds to

Given two three bit number $${a_2}{a_1}{a_0}$$ and $${b_2}{b_1}{b_0}$$ and $$c,$$ the carry in the function that represents the carry generate function when these two numbers are added is

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

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

What is the result of evaluating the following two expressions using three $$-$$ digit floating point arithmetic with rounding? $$\eqalign{ & \left( {113. + - 111.} \right) + 7.51 \cr & 113. + \left( { - 111. + 7.51} \ri...

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

In $$2’s$$ complement addition, the overflow

The $$2's$$ compliment representation of the decimal value $$-15$$ is

The $$2's$$ complement representation of $${\left( { - 539} \right)_{10}}$$ in hexadecimal is

The number $$43$$ in $$2's$$ complement representation is

A graphics card has on board memory of $$1$$ $$MB.$$ Which of the following modes can the card not support?

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

Given $$\sqrt {\left( {224} \right),} = {\left( {13} \right)_r},$$ The value of the radix' $$r$$ is:

Both’s algorithm for integer multiplication gives worst performance when the multiplier pattern is

State the Both's algorithm for multiplication of two numbers, Draw a block diagram for the implementation of the Booth's algorithm for determining the product of two $$8-$$bit signed numbers.