Digital concepts Flashcards
Give one important characteristic of analogue quantities
They can vary over a continuous range of values
Describe Binary digits
- 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
What are logic levels
- the voltages used to represent 1 and 0
- in practice 1 is any voltage between a specified minimum and maximum value
What is the rise time and what is the fall time
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
Equation for duty cycle (%)
Duty cycle = tw/T x 100
T = time period tw = time of HIGH pulse
In Boolean algebra which gate is used as a logic addition
OR gate
y = A + B
(1+1 = 1)
In Boolean algebra which gate is used as a logic multiplication
AND gate
y= A.B
(1 x 0 = 0) (1 x 1 = 0) (0 x 0 = 0)
In Boolean algebra which gate is used as a logic inversion i.e. 1 -> 0 and 0 -> 1
NOT gate
y = A(bar)
What is commutative law of in Boolean Algebra
A + B = B + A
and
A.B = B.A
What is associative law of in Boolean Algebra
A + (B + C) = (A + B) + C
What is distributive law of in Boolean Algebra
A.(B + C) = A.B + A.C
What are DeMorgan’s theorems
First:
(A.B)(all bar) = A(bar) + B(bar)
Second:
(A+B)(all bar) = A(bar).B(bar)
What is the NAND gate
y = A.B(all bar)
multiply then inverse
What is the NOR gate
y = A + B (all bar)
add then inverse
What is the XOR gate
y = A (+) B
Use to find if there is a difference between A and B i.e. 1 if difference, 0 if same
What is the XNOR gate
inverse of XOR gate
Therefore output 1 means A and B are same and 0 means different
Which two forms can any Boolean expression be converted into
- Sum of products (SOP)
- Product of sums (POS)
For both SOP and POS a single over-bar cannot extend for more then one variable
How to determine standard SOP expressions from a truth table
- only consider inputs which combine to get an output of 1
How to determine standard POS expressions from a truth table
- only consider inputs which combine to get an output of 0
What does a comparator do
Performs the magnitude comparison function and compares the magnitudes of two binary numbers
What does an adder do
Adds two binary inputs to make one output
What does an counter do
The counting function counts events represented by changing levels
i.e. if 8 bit counter, can count up to 2^8 = 256, then resets
What does an encoder do
It converts information, such as a decimal number, into a coded form
What does a decoder do
It converts coded information, such as a binary number, into a non coded form, such as a decimal form
Describe the Binary coded decimal (BCD)
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
Describe American standard code for information interchange (ASCII)
It is a 7-bit code, in which the decimal digits are represented by the BCD code preceded by 011
e.g.
8 -> 0111000
Describe Gray code
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
Describe parity method of error detection
- 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
Equation for resolution of a DAC (Digital-to-analogue conversion)
Res = (Vmax - Vmin) / 2^n - 1
n - number of bits
Equation for accuracy of an n-bit DAC
+- 1/2 LSB
LSB = 1/2^n
Equation for resolution of a ADC (analogue-to-Digital conversion)
Res = (Vmax - Vmin) / 2^n
n - number of bits
Definition of Aliasing
when the sampling frequency fs < 2f the output from the ADC gives a false low-frequency waveform called an alias
What is a good sampling rate
fs = 10f
