number systems

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

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

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

Consider a quadratic equation $${x^2} - 13x + 36 = 0$$ with coefficients in a base $$b.$$ The solutions of this equation in the same base $$b$$ are $$x=5$$ and $$x=6$$. Then $$b=$$...

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 representati...

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

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

Zero has two representations in:

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

Consider the number given by the decimal expression. $${16^3} \times 9 + {16^2} \times 7 + 16 \times 5 + 3$$ The number of $$1's$$ in the unsigned binary representation of the numb...