# Questions & Answers of Number representation and computer arithmetic (fixed and floating point)

## Weightage of Number representation and computer arithmetic (fixed and floating point)

Total 13 Questions have been asked from Number representation and computer arithmetic (fixed and floating point) topic of Digital Logic subject in previous GATE papers. Average marks 1.08.

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

b7 b6 b5 b4 b3 . b2 b1 b0

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

## SET-2

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:

00111110011011010000000000000000

The decimal value closest to this floating-point number is

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

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

$\frac{312}{20}=13.1$

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

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

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

Let r denote number system radix. The only value(s) of r that satisfy the equation $\sqrt{{121}_{r}}={11}_{r}$ is / are