Computer Number System Questions with Solutions

${\left(0.57\right)}_8$ in binary is:

${\left(1234\right)}_8$ in hexadecimal is:

Which of the following is equal to ${\left(FF\right)}_{16}$?

Which of the following is the largest?

If ${\left(101\right)}_x={\left(26\right)}_{10}$, then the base $x$ is:

If ${\left(35\right)}_8={\left(y\right)}_{16}$, then $y$ is:

The octal equivalent of ${\left(12.5\right)}_{10}$ is:

Determine the octal equivalent of ${\left(432267\right)}_{10}$

Suppose the largest n-bit number requires 'd' digits in decimal representation. Which of the following relations between 'n' and 'd' is approximately correct?

The binary equivalent of ${\left(531.53125\right)}_{10}$ is

The representation of a floating point binary number +1001.11 in 8 bit fraction and 6 bit exponent format is

Consider the equation ${\left(40\right)}_x={\left(132\right)}_y$ in some bases x and y. Then a possible set of values of x and y is

Consider the equation ${\left(43\right)}_x={\left(y3\right)}_8$, where x and y are unknown. The number of possible solutions is

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

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

Consider the following 4-bit binary numbers represented in the 2's complement form: 1101 and 0100. What would be the result when we add them?

Consider an arbitrary number system with independent digits 0, 1 and A. If we generate the first few numbers in sequence as 00, 01, 0A, 10, 11, 1A and this process is continued to generate the numbers, then the position of 10A is ______

The range of the exponent E in the IEEE 754 double precision (binary64) format is ______

Let the given numbers 11001, 1001 and 111001 correspond to the 2's complement representation. Then with which one of the following decimal numbers do the given numbers match?

Consider a 9-bit representation. Which of the following correctly gives the smallest number that can be represented in (i) 1's complement and (ii) 2's complement?