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2 Column CSS Layout - concise design

Karnaugh Map (K-Map):

One variable, two variable, three variable, four variable:

Representation of truth table on karnaugh map:

Plot k-map fot the expression:

Y = (A+ B+ C+`D) (A+`B+`C+ D) (A+ B+`C+`D) (`A+`B+ C+ D) (`A+`B+`C+ D)

Grouping 2 adjacent cell:

Y=`A`B`C D + A`B`C D

= `B`C D (`A + A ) {RULE `A + A=1}

= `B`C D

Y=`A`BC+`ABC+ABC

=`A`BC+ `ABC+ `ABC+ ABC

=`AC(`B+B)+BC(`A+A) {RULE A+A=A}

=`AC+BC

Grouping 4 adjacent cell:

Y=`AB`CD+ `ABCD+ AB`CD+ ABCD

=`ABD(`C+C) +ABD(`C+C)

=`ABD+ABD

=BD(`A+A)

=BD

Grouping 8 adjacent cell:

Reduce the following expression to its SOP?

Y=`A`B`CD+ `ABCD+ `ABCD+ `ABC`D+ AB`C`D+ AB`CD+ ABCD+ A`BCD?

Reduce the following expression to its POS?

Y=(A+B+`C) (A+`B+`C) (`A+`B+`C) (`A+B+C) (A+B+C)?

UNIT 2 COMBIATIONAL CIRCUIT