Microsoft Word - Digital Logic Design v_4_6a

F = AB.. C+ BA .. C+AB.. C+AB.. C

3) Apply Adjacency Theorem to all pairs as possible.

(another way is drawing double head arrows showing relationship between two terms)

Term ABC ABC AC

Term ABC ABC BC

Term Not Appicable

Term Not Applicable

Term ABC ABC BC

Term ABC BA C CA

( 3 & )4 .. ...

( 2 & )4 .. ...

( 2 & )3

( &1 )4

( &1 )3 .. ...

( &1 )2 .. ...

→ + =

→ + =

→ −

→ −

→ + =

→ + =

Therefore:

F= A.C+B.C+B.C+A.C

4) Perform a second pass of Adjacency theorem.

F= A.C+B.C+B.C+A.C

Therefore:
F= C + C = C

In this case we did not need to apply the Consensus Theorem since the answer cannot be

simplified further.

In general, Systematic Algebraic Reduction (SAR) methods are best suited for computer
programming. K-maps, which will be described in the next section are best suited for human use
up to 4 variables since it is graphic.

c

C^