Data representation Flashcards
What are natural numbers?
Counting objects involves using the numerical symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
These symbols can be used to count objects e.g. 3 little pigs or 10 green bottles.
These values are referred to as natural numbers and we can describe this as a set.
ℕ = {0, 1, 2, 3, …}
What are integer numbers?
Any positive or negative whole numbers are called integers.
Integer values can be described by the set:
ℤ = {…, -2, -1, 0, 1, ….}
What are rational numbers?
Rational numbers (ℚ) include values that can be expressed as fractions or ratios.
This includes:
The set of integers: ℤ
Values with recurring values such as 0.666
We can define rational numbers as decimal or fractional numbers.
What are irrational numbers?
Some numbers (irrational numbers) cannot be expressed exactly as a fraction.
The decimal values of these numbers are endless.
Examples of irrational numbers are π or √ 2.
What are real numbers?
If a number is either rational (an integer or a fraction) or irrational, it is considered to be a real number, ℝ.
A real number is used for measurement.
What are ordinal numbers?
Numbers can be used to describe the position in which values appear, e.g. second, fourth.
These values are called ordinal numbers.
What is the binary number system?
The binary number system uses base 2 and the digits 0 and 1.
Computers can only process instructions in binary.
What is the hexadecimal number system?
Number systems with bases above 10 often still use 0 to 9 but require extra symbols for values past 9.
An example of this is base 16 which is referred to as the hexadecimal number system.
Hexadecimal uses letters for the values 10 to 15.
A = 10
B = 11
C= 12
D = 13
E = 14
F = 15
What are the benefits of hexadecimal?
A hexadecimal value is much easier to read and remember than a string of binary digits.
It is quicker to write or type, since a hex digit takes up only one character, not four.
There is less chance of making an error when typing hex characters than a string of 1s and 0s.
It is used to define colours, in MAC addresses, in assembly languages and machine code.
It is very easy to convert to and from binary.
How do computers work in terms of being an electronic device?
A computer is an electrical device which works in the same way as a light bulb connected to a battery.
Data is stored and processed using combinations of ON and OFF voltages equivalent to a lamp turning on and off where ON = 1 and OFF = 0.
These voltages are “transferred” around the parts of the computer using wires.
How are binary values represented using voltage signals in a computer?
Each individual digit in a binary value is known as a bit (binary digit).
In a computer we can represent binary values using ON and OFF voltage signals for each individual bit.
For n bits a computer can produce 2^n different combinations of values.
One byte = 8 bits
Can represent values from 0-255
What are the different units of data storage?
Historically, storage capacity was expressed using the metric prefixes of kilo (1,000), mega (1,000,000), etc. Since 1998 there has been a move towards using the special prefixes developed to more accurately represent binary values (as per the International System of Units (SI) definition). For example, a kibibyte is equal to 1,024 bytes, whereas a kilobyte is equal to 1,000 bytes.
What is ASCII?
In 1963, the American Standard Code for Information Exchange (ASCII) was established to encode symbols found in the English alphabet.
It was composed of a 7 bit character set giving 2^7 (128) possible binary codes.
Every character on the keyboard is represented by a binary value.
Uppercase letters (capitals) have different values from lowercase characters.
Punctuation symbols have their own characters.
Later, an 8-bit version was developed.
What is a transmission error?
When data is transmitted, it doesn’t always arrive in the same format that it was sent in.
Data transmissions are prone to electromagnetic interference (called noise), and the longer the cable, the more noisy the signal. This can cause a transmission error: when a bit is corrupted, a logic 1 is read as a logic 0, or vice versa.
What are some potential factors which can cause transmission errors?
These errors can cause bits to flip from 0s to 1s and vice versa:
Electrical interference – a disturbance caused by an outside source that degrades the performance of the circuits and can cause them to stop functioning. Can lead to an increase in error rate or complete loss of data.
Power surges – a spike in voltage can cause circuits to be fried and damage hardware, causing transmitted data to potentially be lost.
Synchronisation issues – data errors can result in errors and/or low data quality.
Wear and tear on the cables or connectors.
