Boolean Theorems

In a positive logic circuit

• Logic 0 and 1 represented by 0v (ground) and positive voltage (+VCC respectively )

• Logic 0 and 1 represented by negative and positive voltages respectively

• Logic 0 voltage level is higher than logic 1 voltage level

• Logic 0 voltage level is lower than logic 1 voltage level

In negative logic ,the logic 1 state corresponds to

• High voltage level

• Low voltage level

• Negative voltage level

• Ground level

The following equation corresponds to De Morgan’s theorem in booloen algebra

• (A+B)(A+B)=A+AB+B

• (A+B)(A+B)=AA+AB+BB+BA

• (AB)’=A’+B’

• None of the above

The Boolean algebra is based on the premises that

• Differential equations can be solved by analog circuits

• There are two states

• Data can be stored and retrieved

• None of these

Boolean algebra is different from ordinary algebra in which way?

• Boolean algebra can represent more than 1 discrete level between 0 and 1.

• Boolean algebra have only 2 discrete levels:0 and 1

• Boolean algebra can describe up to levels of logic levels

• They are actually the same

Three managers have a key of a safe with them, and it requires any two keys to open the safe. If A, B and C denote the presence of the three managers respectively in front of the safe, write down the switching expression denoting the condition for opening the safe?

• A.B + B.C + C.A

• (A + B + C) . (A’ + B’ + C’)

• (A + B + C) + B.C + C.A + A.B.C

• All of these

The switching expression F = X’.Y + Y’.Z’ + X.Y + Y’.Z after minimization becomes

• F = X + Y’

• F = X + Y

• F = 0

• F = 1

The dual of the switching expression (X + (Y . 1)) + (Z + 0) is

• (X . (Y + 0)) . (Z . 1)

• (X . (Y + 1)) . (Z . 0)

• (X + (Y + 0)) . (Z + 1)

• None of these

The Boolean expression (A + B)'.(A'+ B')' simplifies to

• A

• B

• 0

• 1

The Boolean expression (X + Y).(X + Y') simplifies to

• X

• Y

• XY

• X'Y'