Below is a question in my homework:

\$F(P,Q,R,S,T)=(P+Q)S+(R+T)\bar S\$ using one or more 2x2 AOI." />

Here's my attempt for (a):

Step 1: simplify boolean expression.

 

\$F(P,Q,R,S,T)\$

 

\$=(P+Q)S+(R+T)\bar S\$

 

\$=PS+QS+R\bar S+\bar ST\$

 

Step 2: expand boolean expression so that it fits into the AOI gate logic:

 

\$F=PS+QS+R\bar S+\bar ST\$

 

\$=\overline{\overline{(PS+QS)+(R\bar S+\bar ST)}}\$

 

\$=\overline{(\overline{PS+QS})(\overline{R\bar S+\bar ST})}\$

I want to know:

1. Do I continue manipulating the boolean expression, or can I just implement the result from Step 2 with AOI gates?

2. Is this double-negate manipulating method suitable for implementing boolean functions with AOI gates (or maybe even all gates in general)?

Any guidance is appreciated!

Below is a question in my homework:

\$F(P,Q,R,S,T)=(P+Q)S+(R+T)\bar S\$ using one or more 2x2 AOI." />

Here's my attempt for (a):

Step 1: simplify boolean expression.

\$F(P,Q,R,S,T)\$

\$=(P+Q)S+(R+T)\bar S\$

\$=PS+QS+R\bar S+\bar ST\$

Step 2: expand boolean expression so that it fits into the AOI gate logic:

\$F=PS+QS+R\bar S+\bar ST\$

\$=\overline{\overline{(PS+QS)+(R\bar S+\bar ST)}}\$

\$=\overline{(\overline{PS+QS})(\overline{R\bar S+\bar ST})}\$

I want to know:

1. Do I continue manipulating the boolean expression, or can I just implement the result from Step 2 with AOI gates?

2. Is this double-negate manipulating method suitable for implementing boolean functions with AOI gates (or maybe even all gates in general)?

Any guidance is appreciated!