Chapter Homework Boolean

Multiple Select Question Select all that apply For which of these triples (x, y, z) does F(x, y, z) = x + yz = 1? (Check all that apply.)

(1, 1, 0) (1, 0, 0) (0, 0, 1) (1, 0, 1)

Multiple Choice Question What do we obtain when we translate the identity (1 + 1) ⋅ 0 = 1 into a logical equivalence?

(T ∨ ¬T) ∧ ¬F ≡ T

Question Mode Multiple Select Question Select all that apply Which of these is correct, where + represents the Boolean sum, ⋅ represents the Boolean product, and 0 = 1 and 1 = 0? (Check all that apply.)

1 ⋅ (1 + 0) = 0 1 ⋅ 0 + 0 ⋅ 1 = 0 ⋅ 0

Select the expressions that are equal to 1, where + represents the Boolean sum and ⋅ represents the Boolean product.

1 ⋅ 1 1 + 1 0 + 1

Multiple Choice Question What do we obtain when we translate the logical equivalence ¬(T ∧ T) ≡ ¬T ∨ ¬T into a Boolean identity?

1⋅1 = 1 + 1

Question Mode Multiple Select Question Select all that apply Which of these statements are true? (Check all that apply.)

A K-map in four variables is a square divided into 16 cells. A product of two Boolean variables corresponds to a block of four cells in a K-map. The K-map of a sum-of-products expansion in four variables can be thought of as lying on a torus.

Multiple Select Question Select all that apply Which of these statements are true? (Check all that apply.)

A combination of input values to a Boolean circuit that never occurs leads to a don't care condition. To find the simplest Boolean function that takes on specified values, we assign 1s to don't care conditions to produce the largest blocks in a K-map. A combination of input values to a Boolean circuit that can never arise leads to a don't care condition.

Fill in the Blank Question What is the value of the expression 1+1⋅1 + 0(1+1⋅1)?

Blank 1: 1

Question Mode Fill in the Blank Question There are (BLANK 1) Boolean functions of degree 2, (BLANK 2) Boolean functions of degree 3, and (BLANK 3) Boolean functions of degree 4.

Blank 1: 16 or sixteen Blank 2: 256 Blank 3: 65536 or 65,536

Question Mode Fill in the Blank Question A K-map in three variables is a rectangle divided into (BLANK 1) cells representing all possible minterms in three variables. Two cells are adjacent if the minterms they represent differ in exactly one literal. A K-map in three variables can be thought of as lying on a (BLANK 2).

Blank 1: eight or 8 Blank 2: cylinder

An (BLANK 1) accepts the value of a Boolean variable as input and produces the complement of this value as output.An (BLANK 2) gate takes the values of two or more Boolean variables as input and produces the Boolean sum of these values as output.An (BLANK 3) gate takes the values of two or more Boolean variables as input and produces the Boolean product of these values as output.

Blank 1: inverter Blank 2: OR or or Blank 3: AND or and

Question Mode Fill in the Blank Question A (BLANK 1)is a Boolean variable or its complement. A (BLANK 2) of the Boolean variables x1, x2, ..., xn is a Boolean product y1y2⋅⋅⋅yn where yi = xi or yi = xi. Such a product (that is, a product of n terms where for each of the nBoolean variables the variable itself or its complement is included) has a value 1 for exactly (BLANK 3)combination of values of its variables.

Blank 1: literal Blank 2: minterm Blank 3: one or 1

Fill in the Blank Question The circuit shown to control a light fixture by flipping either of two switches to turn the light on or off is built using five elements. These are (BLANK 1) _ inverters, (BLANK 2)_ AND gates, and(BLANK 3) _ OR gate. (Fill in the blanks with the numbers of each type of gate.)

Blank 1: two or 2 Blank 2: two or 2 Blank 3: one or 1

Multiple Select Question Select all that apply Which of these pairs of laws is included in the definition of a Boolean algebra?

Identity laws Distributive laws Complement laws Associative laws Commutative laws

Question Mode Multiple Choice Question We can build a circuit that adds two three-bit integers using ______.

one half adder and two full adders

Multiple Select Question Select all that apply Which of these logical statements about the | (NAND) operator are correct? (Check all that apply.)

x = x | x 0 | 1 = 1 | 0 0 | 0 = 1

Question Mode Multiple Choice Question Which of these is the disjunctive normal form of the Boolean function F(x, y, z) where F(0, 0, 0) = F(0, 1, 1) = F(1, 1, 0) = 1 and F(x, y, z) = 0 for all other triples (x, y, z)?

xyz + xyz + xyz