Boolean Algebra
Look Ma! At no time do my hands
leave my arms…
Cleveland Institute of Electronics – Boolean Algebra Lesson
www.cie-wc.edu Call for more info (800) 243-6446
Online distance education.
Boolean Algebra
Original Statement 1
Boolean Algebra
Factor out common term
𝑩 𝑨𝑪 + 𝑨𝑪 + 𝑨𝑫
Boolean Algebra
What remaining has common value?
(part 1)
+
( + )
Boolean Algebra
What remaining has common value?
(part 2)
+
( + )
( + )
Boolean Algebra
Final form for 1
𝑩(𝑪 + 𝑨𝑫)
Boolean Algebra
Original Statement 2
(𝑴 + 𝑵)(𝑴 + 𝑵)
Boolean Algebra
Apply DeMorgan’s Thereom
(𝑴 + 𝑵) + (𝑴 + 𝑵)
Boolean Algebra
That was fun; let’s do it again…
𝑴𝑵 + 𝑴𝑵
Boolean Algebra
Final form 2
+
Boolean Algebra
Original Statement 3
𝑨𝑩𝑪 + 𝑨𝑪
Boolean Algebra
Application of Boolean Theorem
(
+ )
+
= +
+
= +
Boolean Algebra
Final form 3
( + )
Boolean Algebra
Original Statement 4
+
+
+
+
Boolean Algebra
DeMorgan applied to first expression
+
+
+
+
Boolean Algebra
Reorder for grouping
𝑪𝑫 + 𝑨𝑩𝑪 + 𝑨𝑪𝑫 + 𝑨𝑪𝑫 + 𝑨𝑩𝑪𝑫
Boolean Algebra
Collect common terms
( +
)+ (
+
+
Cleveland Institute of Electronics – Boolean Algebra Lesson
)
Boolean Algebra
Regroup to see if something else falls
out
( +
)+ ( ( + )+
( + )=1
)
Boolean Algebra
Everything that is left at this point
( +
)+ ( +
This expression looks like it
could be something for that
tricky theorem…
)
Boolean Algebra
Application of that tricky Boolean
Theorem again
( +
)+
+
= +
Boolean Algebra
Now see what’s left…
𝑪𝑫 + 𝑨𝑩𝑪 + 𝑪𝑫 + 𝑨𝑩𝑪
Boolean Algebra
Reorder for grouping
𝑪𝑫 + 𝑪𝑫 + 𝑨𝑩𝑪 + 𝑨𝑩𝑪
Boolean Algebra
Common terms factored out
( + )+ (
( + )=1
+
)
Boolean Algebra
Final form 4
+ (
+
)=
+
+
Cleveland Institute of Electronics – Boolean Algebra Lesson
www.cie-wc.edu Call for more info (800) 243-6446
Online distance education.