Question $1$

$($a$)$ State whether the following statements are correct or not. Show your work.

i$.(49{)}_{10}=(31{)}_{16}=(110001{)}_2,$ Show your work.

ii$.7B_{16}=(1111011{)}_2=(123{)}_{10},$ show your work.

$($b$)$ If you have the binary number $1101\mathrm{.}01112,$ what will be its decimal number equivalent to$?$ Show your work.

$[2]$

$($c$)$ Convert ${61453}_{10}$ to hexadecimal system, show your work.

$[4]$

$($d$)$ A given number in base $x$ can be converted to any other base $y.$ According to the expansion method, if abc.$de$ is any given number in base $x,$ then write its value in base $10.$ Show your work.

$[2]$

$($e$)$ find te value of $x$ if ${13}_x+{82}_x={17}_{10}.$ Show your work

$[3]$