Consider a quaternary, normalized floating$-$point number system that is base $4$ with chop$-$

ping. Analogous to a bit, a quaternary digit is a quit. Assume that a hypothetical quaternary

computer uses the following floating$-$point representation:

sm se e$1$ e$2$ q$1$ q$2$ q$3$ q$4$

where sm is the sign of the mantissa and se is the sign of the exponent $(0$ for positive, $1$

for negative$),$ q$1,$ q$2,$ q$3$ and q$4$ are the quits of the mantissa, and e$1,$ e$2$ are the quits of the

exponent, an integer, and each quit is $0,1,2$ or $3.$ Show all your work for all parts.

$1$

$($a$)$ What is the computer representation of $7\mathrm{.}187510$ in this system?

$($b$)$ What decimal value does $00101321$ represent in this system?

$($c$)$ Let p be a real number in the interval $[6410,25610).$ If we need to represent p in

this quaternary floating$-$point system with some p$,$ what is the upper bound on the

absolute error of this representation? Your answer should be in decimal