Lecture 1 - Binary and Boolean Algebra

Question 1

Define the term “Analog”

Answer 1

Infinite number of increments and/or possibilities

Question 2

Define the term “Digital”

Answer 2

Means that there is a limited set of values by which something can be represented

Question 3

What does 0 represent in the binary number system?

Answer 3

ON

Question 4

What does 1 represent in the binary number system?

Answer 4

OFF

Question 5

MSB

Answer 5

Refers to the outermost left bit and stands for “Most Significant Bit”

Question 6

LSB

Answer 6

Refers to the outermost right bit and stands for “Least Significant Bit”

Question 7

How is the binary number system different from the decimal number system?

Answer 7

Where the decimal number system has 10 symbols to be represented with (0 to 9) the binary number system only has two (0 to 1)

Question 8

Nibble

Answer 8

Group of 4 bits

Question 9

Byte

Answer 9

Group of 8 bits

Question 10

Word

Answer 10

Another group of bits where the length is processor dependant (depends on what processor we’re looking at)

Question 11

How many numbers can be represented in a n-bit word?

Answer 11

The number of states which can be represented are: 2^n ; (0 - 2^n)

Question 12

What formula is used to calculate the amount of bits needed to represent a number?

Answer 12

Since the highest number to be represented is found using the formula: y = 2^n - 1, therefore to find the number of bits to represent it: n = log[2] (y + 1) ; log base 2

Question 13

What do the 0s and 1s represent in a digital signal?

Answer 13

They represent a range of voltages (since the signals are waves, as long as the voltage is within a range it will either be on or off)

Question 14

Grey Zone

Answer 14

Interpretable region in a digital signal graph which is outside of the ON voltage and OFF voltage range (sandwiched in between)

Question 15

Accuracy (Analog vs. Digital)

Answer 15

Analog: 0.1% is considered a very good accuracy
Digital: Accuracy is directly proportional to the amount of circuitry added

Question 16

Long Term Storage (Analog vs. Digital)

Answer 16

Analog: Store data as voltage on a capacitor (short term for an approximate maximum of 30 mins)
Digital: Stores data in memory (long term can last up to years)

Question 17

Speed (Analog vs. Digital)

Answer 17

Most common use of analog or digital
Analog: Fastest circuits, high-frequency, etc

Question 18

Define “Analog Signals”

Answer 18

Smooth, continuous waves that can have any value within a range, like turning up the volume smoothly.

Question 19

Define “Digital Signals”

Answer 19

Step-like signals that are either on or off, high or low, representing information using distinct levels, like flipping a light switch.

Question 20

What is Boolean Algebra

Answer 20

Two-value algebra; values of either 0 or 1

Question 21

AND

Answer 21

(ab) = X is 1 if both a and b are 1

Question 22

OR

Answer 22

(a + b) = X is 1 if a or b or both are 1

Question 23

XOR

Answer 23

X is 1 if exactly one of a or b are 1 (not both; essentially OR with an extra condition)

Question 24

NAND

Answer 24

X is 0 if both a and b are 1

Question 25

NOR

Answer 25

X is 0 if either a or b or both are 1

Question 26

X-NOR

Answer 26

X is 0 if exactly one of a or b are 1

Question 27

Absorption Laws (S1)

Answer 27

XY + X = X

Question 28

Dual Absorption Laws (S2)

Answer 28

(X + Y) X = X

Question 29

Basic Laws (B1) and (B2) and their Dual Form (B3) and (B4)

Answer 29

X + 0 = X (B1)
X + 1 = 1 (B2)

X (1) = X (B3)
X (0) = 0 (B4)

Question 30

Idempotent (I1)

Answer 30

A variable is unchanged by operating with itself
X + X = X

Question 31

Dual Idempotent (I2)

Answer 31

X (X) = X

Question 32

Commutative Laws (C1)

Answer 32

X + Y = Y + X

Question 33

Dual Commutative Laws (C2)

Answer 33

(X) (Y) = (Y) (X)

Question 34

Associative Laws (A1)

Answer 34

X + (Y + Z) = (X + Y) + Z

Question 35

Dual Associative Laws (A2)

Answer 35

(X) (YZ) = (XY) (Z)

Question 36

Distributive Laws (D1)

Answer 36

(X + Y) (Z) = (XZ) + (YZ)

Question 37

Dual Distributive Laws (D2)

Answer 37

(XY) + Z = (X + Z) (Y + Z)