EXERCISE

$1\mathrm{.}9$ Consider a $4-$bit digital word $D=b_3{b}_2{b}_1{b}_0($see Eq$.1\mathrm{.}3)$ used to represent an analog signal $y_4$ that varics between $0$ V and $+15$ V $.$

$($a$)$ Give $D$ corresponding to

$()1,$ and $15$ V $.$

$($b$)$ What change in $v_1$ causes a change from $0$ to $1$ in $($i$)b_0,($ii$)b_1,($iii$)b_2,$ and $($iv$)b_3?$

$($c$)$ If $v_A=5\mathrm{.}2V,$ what do you expect $D$ to be$?$ What is the resulting error in representation?

Ans. $($a$)0000,0001,0010,1111$; $($b$)+1V,+2V,+4V,+8V$; $($c$)0101,-4\%$