QUIZ 2.1:
Boolean Algebra Basics

QUIZ 2.1 Boolean Algebra Basics

Instruction: Read each item carefully and select the best answers. Hit the submit button once you are done.

The output of the expression $$(x+y+z)(\bar{x}\cdot\bar{y}\cdot\bar{z})$$ for all input combinations is

Always true

Mostly true

Mostly false

Always false

Given the following boolean statements, determine the incorrect statement below.

$$x+x=x$$

$$x+1=1$$

$$x\cdot y=y\cdot x$$

$$x+\overline{x}=1$$

A demonstrates Idempotent Law

B demonstrates Domination Law

C demonstrates Commutative Law

D demonstrates Identity Law

Which of the following is false?

$$\overline{(m+n)}=\overline{m}\cdot \overline{n}$$

$$x(y+z)=(x+y)(x+z)$$

$$c(defgh)=h(efg)(cd)$$

$$A+(\overline{A}B)=A+B$$

Which of the following boolean equations has no solution?

$$x\cdot 1 = 0$$

$$x + x = 0$$

$$1 \cdot x = x$$

$$x \cdot \overline{x} = 1$$

Given $$F(x,y,z)=x\overline{y}+\overline{xyz}$$. Which of the following input combination evaluates 0?

$$F(0,0,0)$$

$$F(1,0,1)$$

$$F(0,1,0)$$

$$F(1,1,1)$$

Which of the following is incorrect?

$$1\cdot \overline{0} = 1$$

$$1+ \overline{1} = 1$$

$$\overline{0} \cdot 0 = 0$$

$$\overline{(1+0)} = 1$$

The boolean operator $$\oplus$$ behaves the same way as a logical Exclusive OR (XOR) operator. Which of the following always evaluates to $$\overline{x}$$ for all values of $$x$$?

$$0\oplus x$$

$$x\oplus x$$

$$x\oplus 1$$

$$\overline{x}\oplus x$$

The simplified form of the boolean expression ABD+CD+ACD+ABC+ABCD is:

AB(C+D)+CD

CD(A+B)+AB

C(A+B+D)+CD

D(AB+C+AC+AB+ABC)

The statement $$AC+ABC=AC$$ holds true by the ______ law.

Evaluate the expression $$(\bar{1}\cdot\bar{0})+(\overline{1\cdot0}+0)$$ .

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- EZ Tutorial Team

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