Question $43$

BOOLEAN ALGEBRA

a$)$ For the function $F(ABC)={}_m(2,4,5,6,7),$ find the following:

i$)$ The standard SOP form

$[1$ mark$]$

ii$)$ The minimum SOP form $($using Boolean algebra only$)$

$[4$ marks$]$

iii$)$ The minimum SOP form using a Karnaugh Map

$[4$ marks$]$

Simplify the following expressions:

i$)Y=\frac{A}{b}ar(B)D+\frac{A}{b}ar\frac{B}{b}ar(D)$

$[3$marks$]$

ii$)Z=(\frac{?}{\text{b}\text{a}\text{r}}(A)+B)(A+B)$

$[3$marks$]$

iii$)W\frac{?}{b}=ar((A+BC)(D+EF))$

$[5$ marks$]$

Map the following standard SOP expression on a Karnaugh map:

i$)\frac{?}{\text{b}\text{a}\text{r}}\frac{A}{b}ar(B)C\frac{+}{b}ar(A)\frac{B}{b}ar(C)+A\frac{B}{b}ar(C)+$ABC

$[2$ marks$]$

ii$)\frac{?}{\text{b}\text{a}\text{r}}\frac{A}{b}ar(B)CD\frac{+}{b}ar(A)\frac{B}{b}ar\frac{C}{b}ar(D)+A\frac{B}{b}ar(C)D+$ABCD$+A\frac{B}{b}ar\frac{C}{b}ar(D)\frac{+}{b}ar\frac{A}{b}ar\frac{B}{b}ar(C)D+\frac{A}{b}ar(B)\frac{C}{b}ar(D)[3$ marks$]$