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02 - De Morgans Laws

 1. Select which of the following options (1,2,3,4) fits when DeMorgan's laws are applied:
Note: In this notation the "~" is a 'NOT'

~(A * B) = 

1. ~A + ~B

2. ~A * ~B

3. A * B

4. ~A * B 

  4

  3

  2

  1

 2. Apply DeMorgan's laws to: ~(A + B) =
Note: In this notation the "~" is a 'NOT'

~(A + B) = 

1. ~A + ~B

2. ~A * ~B

3. A * B

4. ~A * B 

  2

  4

  1

  3

 3. DeMorgan’s theorem may be thought of in terms of breaking __________

  A + sign

  the rules of boolean algebra

  the commutative law

  A long bar symbol

 4. When multiple “layers” of bars exist in an expression, you may only break one bar at a time, and it is generally easier to begin simplification by breaking the longest (uppermost) bar first

  TRUE

  FALSE

 5. Use DeMorgan's law on the expression: DE + ~D + ~E and you will get: DE + D* ~E

  TRUE

  FALSE

 6. You should never break more than one bar in a single step

  TRUE

  FALSE

 7. Fill in the blanks in this excerpt that explains what DeMorgan's Theorems describe
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 XOR gate

  Negative-AND gate.

  negative - OR Gate

  positive OR Gate

 8. DeMorgan's laws: Two separate terms NAND´ed together is the same as the two terms inverted (Complement) and ___________

  OR´ed

  XOR'ed

  AND'ed

  further inverted again

 9. Analyse the first two steps provided below and fill in the blanks for 1 and 2.
demorganslaws1.png

  1 = signs 2 = OR'ing

  1 = signs 2 = converted

  1 = shapes 2 = inverted

  1 = shapes 2 = redirected

 10. Given that F = A'B'+ C'+ D'+ E', which of the following represent the only correct expression for F'?
Note: In this notation we use the ' to denote negation

  F'= A+B+C+D+E

  F'= AB(C+D+E)

  F'= AB+C'+D'+E'

  F'= (A+B)CDE

 11. What part of this table, on careful analysis, proves that DeMorgan's theorem is correct?
demorganslaws2.png

  every single column contains at least one '1' which proves the theorem

  columns 5,9 and 10 contain only one 0, which proves the theorem

  column no 7 and 8 are equal and column no 9 and 10 are also equal

  columns 6 and 7 are inverse to each other

 12. Not (A and B) is the same as Not A ___ Not B.

  not

  or

  nor

  and

 13. Read the rather long question below to use DeMorgan's laws to solve this 'real world' problem.
A recent survey asked high school students whether 
or not they planned to go to the upcoming basketball
 game or the upcoming football game.

200 total students were surveyed.

58 students stated that they would miss at 
least one of the games (this includes the 
students that plan to miss both games).

How many students plan to attend both games?

By De Morgan's Laws, this set of 58 students is 
the complement of the set of students who will 
attend both games.

Therefore, the number of students who will attend 
both games is:

  58 - 58 = 0

  200 + 58 = 142 and 200 - 142 = 58

  58 + 58 = 116

  200 - 58 = 142

 14. By De Morgan's Laws, A NAND B is equivalent to~A OR ~B (The overline represents the negation of a signal). Thus, an OR gate can be constructed by ______________________
demorganslaws3.png

  inverting each output of an AND gate

  negating each input of a NAND gate.

  negating each output of an OR gate

  inverting each input of an OR or NOR gate

 15. Augustus De Morgan, credited with formulating DeMorgan's laws, was born in _____________ in 1806

  Paris, France

  Jerusalem, Israel

  London, England

  Madurai, India