Tugas 6 Bravo 2103015233 Teorema DeMorgan's
Nama: Bravo
Marvel
Kelas: 2B
NIM:
2103015233
Rangkuman Teorema DeMorgan's
Teorema DeMorgan’s(De Morgan’s theorem)
DeMorgan’s theorem may be thought of in
terms of breaking a
long bar symbol.
When a long bar is broken, the operation directly underneath the
break changes from addition to multiplication, or vice versa, and the broken
bar pieces remain over the individual variables.
When multiple “layers” of bars exist in an expression, you may only break one bar at a time, and it generally easier to begin simplificatiaon by breaking the longest (uppermost) bar first.
You should never break more than one bar in a single step.
As tempting as it may be to conserve steps
and break more than one bar at a time, it often leads to an incorrect result,
so don’t do it!
It is possible to properly reduce this expression by breaking
the short bar first, rather than the long bar first
Review
·
DeMorgan’s Theorems
describe the equivalence between gates with inverted inputs and gates with
inverted outputs. Simply put, a NAND gate is equivalent to a Negative-OR gate,
and a NOR gate is equivalent to a Negative-AND gate.
·
When “breaking” a
complementation bar in a Boolean expression, the operation directly underneath
the break (addition or multiplication) reverses, and the broken bar pieces
remain over the respective terms.
·
It is often easier to
approach a problem by breaking the longest (uppermost) bar before breaking any
bars under it. You must never attempt
to break two bars in one step!
· Complementation bars function as grouping symbols. Therefore, when a bar is broken, the terms underneath it must remain grouped. Parentheses may be placed around these grouped terms as a help to avoid changing precedence.
Questions & answers:
1.
Using DeMorgan's law,
which of the following is equivalent to the statement?
A′∩B
A.
AuB
B.
(AnB)
C.
(AuB’)’
D.
A’uB’
Answer: C
2. Which of the following scientist represented De-
Morgans theorem?
A.
August De-morgan
B.
Charles De-morgan
C.
Richard De-morgan
D.
None of the above
Answer: A
3. De-morgans theorem solves _____ expressions?
A. Boolean algebra
B. Logic gates
C. Aritmetic
D. Both a and b
Answer: D
4. De-morgans theorem is applicable for _____ types
of components?
A. High circuit design
B. computer programming
C. computer hardware
D. both a and b
Answer: D
5. Logic high in Boolean language is represented
with _____?
A. Logic 0
B. Logic 1
C. Logic x
D. None of the above
Answer: B
6. Which of the following processes used in solving
De-Morgans theorem?
A. Truth tables
B. Logical expressions
C. Logic gates
D. Both a and b
Answer: D
7. According to De-Morgans theorem an inverted AND
gate operation result is similar to _____ type of logic gate operation?
A. OR
B. NOT
C. XOR
D. NOR
Answer: B
8. Which of the following logical operation of does
a De-Morgans theorem performs?
A. AND
B. OR
C. NOT
D. All the above
Answer: D
9. Which of the following is the De-Morgans formula
for (X.Y)’?
A. X’ + Y’
B. X’ – Y’
C. X’ * Y’
D. X’/Y’
Answer: A
10. A NAND
gate in De-Morgans formula for (X.Y)’ is also called ___?
A. Bubbled OR
B. Bubbled NOR
C. Bubbled XOR
D. Bubbled NOT
Answer: A
11. De-Morgans
theorem can be verified using _____?
A. Logic gates
B. Truth table
C. Graphs
D. Both a and b
Answer: D
12. A truth
table is a ______ table?
A. Mathematical
B. Logical
C. Boolean
D. All the above
Answer: D
13. A truth
table has ___ number of columns for each input variable?
A. 1
B. 2
C. 3
D. 4
Answer: A
14. A truth table has _____ number of unary
operations?
A. 1
B. 2
C. 3
D. 4
Answer: D
15. A never
true of unary operation is also called ___?
A. Unary falsum
B. Unary identity
C. Unary negation
D. Unary true
Answer: A
16. Which of
the following is the negation value of ‘true’?
A. True
B. False
C. Don’t care
D. None of the above
Answer: B
17. Which of
the following is the negation value of ‘false’?
A. True
B. False
C. Don’t care
D. None of the above
Answer: A
18. Which of
the following is the output of AND gate if input is (0,0)?
A. 0
B. 1
C. x
D. None of the above
Answer: A
19. Which of
the following is the output of AND gate if input is (0,1)?
A. 0
B. 1
C. x
D. None of the above
Answer: A
20. Which of
the following is the output of AND gate if input is (1,0)?
A. 0
B. 1
C. x
D. None of the above
Answer: A
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