Digital concepts

Question 1

Give one important characteristic of analogue quantities

Answer 1

They can vary over a continuous range of values

Question 2

Describe Binary digits

Answer 2

• The two digits of the binary system are 1 and 0, these are called bits
• Two different voltage levels are used to represent the two

HIGH = 1 LOW = 0

• Combinations of bits are called codes and are used to represent; numbers, letters, symbols, instructions

Question 3

What are logic levels

Answer 3

• the voltages used to represent 1 and 0

- in practice 1 is any voltage between a specified minimum and maximum value

Question 4

What is the rise time and what is the fall time

Answer 4

rise time: time required for a digital pulse to go from LOW to HIGH

fall time: time required for a digital pulse to go from HIGH to LOW

Question 5

Equation for duty cycle (%)

Answer 5

Duty cycle = tw/T x 100

T = time period
tw = time of HIGH pulse

Question 6

In Boolean algebra which gate is used as a logic addition

Answer 6

OR gate

y = A + B

(1+1 = 1)

Question 7

In Boolean algebra which gate is used as a logic multiplication

Answer 7

AND gate

y= A.B

(1 x 0 = 0) (1 x 1 = 0) (0 x 0 = 0)

Question 8

In Boolean algebra which gate is used as a logic inversion i.e. 1 -> 0 and 0 -> 1

Answer 8

NOT gate

y = A(bar)

Question 9

What is commutative law of in Boolean Algebra

Answer 9

A + B = B + A
and
A.B = B.A

Question 10

What is associative law of in Boolean Algebra

Answer 10

A + (B + C) = (A + B) + C

Question 11

What is distributive law of in Boolean Algebra

Answer 11

A.(B + C) = A.B + A.C

Question 12

What are DeMorgan’s theorems

Answer 12

First:
(A.B)(all bar) = A(bar) + B(bar)

Second:
(A+B)(all bar) = A(bar).B(bar)

Question 13

What is the NAND gate

Answer 13

y = A.B(all bar)

multiply then inverse

Question 14

What is the NOR gate

Answer 14

y = A + B (all bar)

add then inverse

Question 15

What is the XOR gate

Answer 15

y = A (+) B

Use to find if there is a difference between A and B i.e. 1 if difference, 0 if same

Question 16

What is the XNOR gate

Answer 16

inverse of XOR gate

Therefore output 1 means A and B are same and 0 means different

Question 17

Which two forms can any Boolean expression be converted into

Answer 17

• Sum of products (SOP)
• Product of sums (POS)

For both SOP and POS a single over-bar cannot extend for more then one variable

Question 18

How to determine standard SOP expressions from a truth table

Answer 18

• only consider inputs which combine to get an output of 1

Question 19

How to determine standard POS expressions from a truth table

Answer 19

• only consider inputs which combine to get an output of 0

Question 20

What does a comparator do

Answer 20

Performs the magnitude comparison function and compares the magnitudes of two binary numbers

Question 21

What does an adder do

Answer 21

Adds two binary inputs to make one output

Question 22

What does an counter do

Answer 22

The counting function counts events represented by changing levels

i.e. if 8 bit counter, can count up to 2^8 = 256, then resets

Question 23

What does an encoder do

Answer 23

It converts information, such as a decimal number, into a coded form

Question 24

What does a decoder do

Answer 24

It converts coded information, such as a binary number, into a non coded form, such as a decimal form

Question 25

Describe the Binary coded decimal (BCD)

Answer 25

A method of expressing decimal numbers
decimal digits are represented by a binary code of 4 bits

Decimal BCD
0 0000
1 0001
2 0010
3 0011
8 1000
9 1001

Question 26

Describe American standard code for information interchange (ASCII)

Answer 26

It is a 7-bit code, in which the decimal digits are represented by the BCD code preceded by 011

e.g.
8 -> 0111000

Question 27

Describe Gray code

Answer 27

Important feature of Gray code is that it only exhibits a single bit change from one number to the next

3-bit binary 3-bit Gray
000 000
001 001
010 011
011 010
100 110
101 111

Question 28

Describe parity method of error detection

Answer 28

• a parity bit is attached to a group of bits to make the number of 1s, including the parity bit, always even or always odd.

i.e.
even parity:
8 –> 1 1000

odd parity:
8 –> 0 1000

A parity bit can only detect a one bit error

Question 29

Equation for resolution of a DAC (Digital-to-analogue conversion)

Answer 29

Res = (Vmax - Vmin) / 2^n - 1

n - number of bits

Question 30

Equation for accuracy of an n-bit DAC

Answer 30

+- 1/2 LSB

LSB = 1/2^n

Question 31

Equation for resolution of a ADC (analogue-to-Digital conversion)

Answer 31

Res = (Vmax - Vmin) / 2^n

n - number of bits

Question 32

Definition of Aliasing

Answer 32

when the sampling frequency fs < 2f the output from the ADC gives a false low-frequency waveform called an alias

Question 33

What is a good sampling rate

Answer 33

fs = 10f