Question

A $2-$bit flash Analog to Digital Converter (ADC) is given below. The input is $0<V_{IN}<3$ volts. The expression for the LSB of the output $B_o$ as a Boolean function of $X_2,X_1$ and $X_0$ is

Answer 1

The inputs to digital circuit are $X_2,X_1,X_0$ and outputs are $B_1,B_0$

$X_2$	$X_1$	$X_0$	$B_1$	$B_0$
$0$	$0$	$0$	$0$	$0$
$0$	$0$	$1$	$0$	$1$
$0$	$1$	$1$	$1$	$0$
$1$	$1$	$1$	$1$	$1$

$B_o={\overline{X}}_2{\overline{X}}_1{X}_0+X_2{X}_1{X}_0$
$=X_o({\overline{X}}_2{\overline{X}}_1+X_2{X}_1)$
$=X_0\left(\overline{X_2⨁X_1}\right)$