In many communication and networking systems, the signal transmitted on

the communication line uses a non$-$return$-$to$-$zero $($NRZ$)$ format. USB

uses a specific version referred to as non$-$return$-$to$-$zero inverted $($NRZI$).$

A circuit that converts any message sequence of Os and ls to a sequence in

the NRZI format is to be designed. The mapping for such a circuit is as

follows:

$($a$)$ If the message bit is a $0,$ then the NRZI format message contains an

immediate change from $1$to$0$ or from $0$ to $1,$ depending on the current

NRZI value.

$($b$)$ If the message bit is a $1,$ then the NRZI format message remains fixed at

$0$or $1,$ depending on the current NRZI value.