GATE EC 2015 Set 3 Q49 — Number Representations

What is the $10^{\prime} s$ complement of $(47)_{10}?$

In a number system of base $r$, the equation $x^{2}-12 x+37=0$ has $x=8$ as one of its solutions. The value of $r$ is $\_\_\_\_\_\_\_$.

​​​​​​​If $(1235)_{x}\:=\:(3033)_{y}$, where $x$ and $y$ indicate the bases of the corresponding numbers, then

The number of bytes required to represent the decimal number $1856357$ in packed BCD (Binary Coded Decimal) form is ___________.

$\mathrm{X}=01110$ and $\mathrm{Y}=11001$ are two $5$-bit binary numbers represented in two's complement format. The sum of $\mathrm{X}$ and $\mathrm{Y}$ represented in two's complement format using $6$ bits is

A new Binary Coded Pentary (BCP) number system is proposed in which every digit of a base-$5$ number is represented by tis corresponding $3$-bit binary code. For example, the base-$5$ number $24$ will be represented by its BCP code $010100.$ In this numbering system, the BCP code $100010011001$ corresponds to the following number in base-$5$ …