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

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

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____________.


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

In the IEEE floating point representation the hexadecimal value 0x00000000 corresponds to

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