Data Representation Flashcards
Natural numbers
- All positive whole numbers and zero
- Used for counting
Integer numbers
All whole numbers, including zero
Rational numbers
- Numbers that can have a fractional part
- Includes zero
Irrational numbers
Numbers that cannot be written exactly as a fraction
Real numbers
- All possible real world quantities
- All members of irrational, rational, integers and natural numbers are real numbers
Ordinal numbers
Integers used to describe the numerical positions of objects in relation to others
Decimal
- Uses the digits 0 through 9
- Denoted with subscript 10
Binary
- Uses the digits 0 and 1
- Can represent high and low currents
- Denoted with subscript 2
Hexadecimal
- Uses the digits 0 through to 9 followed by the uppercase characters A to F
- Denoted with a subscript 16
- Can represent numbers using far fewer digits than binary or even decimal
Bit
- The fundamental unit of information
- Represents high or low current
- Can take either of the values 0 and 1
- The more bits assigned to a number, the more values can be represented
Byte
8 bits
Nibble
4 bits
Binary prefixes
Go up in powers of 2
Denary prefixes
Go up in powers of 10
Unsigned binary numbers
Can only represent positive numbers
Signed binary numbers
Can also represent negative numbers
Range of unsigned binary numbers
0 to 2^n - 1
Two’s complement
- The MSB is given a negative place value
- Has a range of 2^(n-1) to -2^(n-1)
Information coding system
The method computers follow to represent characters
Character code
A decimal digit used to represent a character
ASCII
- A character encoding system that is used to represent English characters
- Uses 7 bits to represent 128 different characters
Unicode
- A character encoding system that is used to represent text from all languages (and other symbols)
- Uses anywhere from 8 to 48 bits per character
Error checking methods
- Parity bits
- Majority voting
- Checksums
- Check digits
Parity bits
- A single bit added to a transmission that can be used to check for errors in transmitted data
- Can use even or odd parity
- If an error is detected the computer asks the sender to retransmit the data
Even parity
The parity bit makes the total number of 1s in the transmitted data even
Odd parity
The parity bit makes the total number of 1s in the transmitted data odd
Issue with parity bits
If an even number of bits are changed during transmission, the error is not detected
Majority voting
- Each bit of the data is transmitted multiple times with the most commonly occurring value taken to be correct
- Majority voting doesn’t just detect errors, it also corrects them
Issues with majority voting
- The volume of data being transmitted is increased, increasing the time taken to
transmit data - If multiple bits are changed then the transmission can still be incorrect
Checksums
- A value is appended to the transmitted data, determined by the data itself
- Once received the recipient removes the checksum and carries out a check to ensure the checksum is correct
- If the 2 do not match the sender must re-transmit the data
Check digits
- An extra digit added to the end of a number that detects errors
- It is calculated by performing a mathematical formula based on the other digits
Representing data
Computers use bit patterns to represent all forms of data
Analogue signals
Can take any values and can change as frequently as required
Digital signals
Must always take one of a specified range of values and can only change value at specified intervals
Digital to analogue conversion
- Uses a digital to analogue converter
- The device reads a bit pattern representing an analogue signal
- Outputs an alternating, analogue, electrical current
Analogue to digital conversion
- Uses an analogue to digital converter
- The device takes a reading of an analogue signal at regular intervals and records the value
- Samples are taken at a specific frequency
Sampling
The process of measuring the magnitude of an analogue signal at regular intervals
Sampling rate
The number of samples taken per second
Sample resolution
The number of bits used to store each sample
Bitmap graphics
Images made up of many individual pixels
Pixels
- The smallest individually addressable point on an image
- Has an assigned binary value that determines the color of the pixel
Resolution
- Pixels per square inch
- Total number of pixels in an image
Color depth
- The number of bits assigned to a pixel
- n pixels can represent 2^n different colours
Metadata
Additional information about an image, e.g date created
