Session 2: Exercises

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Exercise1. Obtain in the truth table the result column of any of these functions:

 


Exercise 2. Show the main theorems used in the perfect induction method. This is, complete the corresponding columns in the truth table and make sure that they are identical.

Single Variable Theorem


 

Two variables Theorem


 

Three variables Theorem



Extended Demorgan Theorem


 

Exercise 3. Write beside each equality True (T) or False (F).


 

Exercise 4. Analyse the following circuit obtaining its truth table.

 

B3

B2

B1

B0

X3

X2

X1

X0

0

0

0

0

 

 

 

 

0

0

0

1

 

 

 

 

0

0

1

0

 

 

 

 

0

0

1

1

 

 

 

 

0

1

0

0

 

 

 

 

0

1

0

1

 

 

 

 

0

1

1

0

 

 

 

 

0

1

1

1

 

 

 

 

1

0

0

0

 

 

 

 

1

0

0

1

 

 

 

 

1

0

1

0

 

 

 

 

1

0

1

1

 

 

 

 

1

1

0

0

 

 

 

 

1

1

0

1

 

 

 

 

1

1

1

0

 

 

 

 

1

1

1

1

 

 

 

 

Exercise 5. Analyse the following circuit obtaining its truth table.

 

 

EI

A2

A1

A0

S7

S6

S5

S4

S3

S2

S1

S0

0

0

0

0

 

 

 

 

 

 

 

 

0

0

0

1

 

 

 

 

 

 

 

 

0

0

1

0

 

 

 

 

 

 

 

 

0

0

1

1

 

 

 

 

 

 

 

 

0

1

0

0

 

 

 

 

 

 

 

 

0

1

0

1

 

 

 

 

 

 

 

 

0

1

1

0

 

 

 

 

 

 

 

 

0

1

1

1

 

 

 

 

 

 

 

 

1

0

0

0

 

 

 

 

 

 

 

 

1

0

0

1

 

 

 

 

 

 

 

 

1

0

1

0

 

 

 

 

 

 

 

 

1

0

1

1

 

 

 

 

 

 

 

 

1

1

0

0

 

 

 

 

 

 

 

 

1

1

0

1

 

 

 

 

 

 

 

 

1

1

1

0

 

 

 

 

 

 

 

 

1

1

1

1