Question $5$

$(14$ marks$)$

$($a$)$

TABLE $1$

In communication, a technique of code conversion is used so that no more than three $0\text{'}$s are

present in a code. An example is called $4$B$5$B code conversion as shown in Table $1.$ Assume that

the $4-$bit input codes are labelled ABCD and the $5-$bit output codes as KLMNO.

Using the Karnaugh map to find the simplest Boolean expressions for $K$ and $N.$

$($b$)$

Given a Boolean expression $Y$ as follows.

$Y\frac{?}{b}=ar(B)\frac{*}{b}ar(C)\frac{+}{b}ar(A)*B*C+A*B\frac{+}{b}ar(A)\frac{*}{b}ar(C)$

$($i$)$ Draw the Karnaugh map of Y$.$

$($ii$)$ Use your result in $($i$)$ to find the simplest expression of Y$.$

$($iii$)$ Implement $Y$ with NAND gates only and draw the circuit diagram.