Topic 5 - Fundamentals of Data Representation Flashcards
What are natural numbers?
Natural numbers are a set of whole numbers consisting of positive numbers as well as zero.
What is the symbol for a natural number set?
ℕ is the symbol for natural numbers.
Define a set.
A set is an unordered collection of data which contains each item only once.
What are integer numbers?
Integer numbers are a set of whole numbers consisting of positive and negative numbers as well as zero.
Give the symbol of an integer number set.
ℤ is the symbol for integer numbers.
What are rational numbers?
Rational numbers (a.k.a quotients) are a set of numbers consisting of positive and negative numbers as well as zero. Rational numbers can be in the form of a fraction or decimal.
Give the symbol for a rational numbers set.
ℚ is the symbol for rational numbers.
Define irrational numbers.
Irrational numbers are opposite to rational numbers as they can’t be expressed as fractions and are never-ending and non-repeating; e.g. π, √2. Irrational numbers DON’T have a symbol.
Describe the real numbers set.
Real numbers are a number set consisting of all the number word quantities; integer, natural, irrational and natural number sets are all in the real number set.
State the real numbers set symbol.
ℝ is the symbol for real numbers.
What are ordinal numbers?
Ordinal numbers are a set of numbers which specify positions for certain quantities or objects; e.g. 1st, 2nd, 3rd, 4th…
Give a use of natural numbers.
Natural numbers are used in counting quantities or things as you can’t count using negative numbers but you can using positive numbers.
Give a use of real numbers.
Real numbers are used in measuring quantities because not every accurate measurement is a whole number; there are many measurements that are in the form of a decimal.
What are number bases?
Number bases are simply differing forms of representation of numbers.
Define the denary number system.
Denary, also known as decimal, number system is a system extending from 0 to 9 and is used by humans. It is a base 10 system.
Describe the binary number system.
The binary number system is a system used by computers consisting of only two digits: 0 and 1. It is used to process data for the computer to understand. This system is base 2.
Describe the hexadecimal number system.
The hexadecimal number system is a system which extends from 0 - 9 but uses uppercase characters to represent the decimal numbers from 10 to 15. It is a base 16 system and the most compact of all the systems as it can easily represent huge numbers in smaller ways.
Describe how to convert a binary number to a denary number.
Write down the binary number with each integer spaced apart a little, and above each 1 or 0, write a place value header (a collection of values starting from the right, and increasing in powers of 2). Next, take note of any place value headers with a 1 below them and at the end, add these headers, giving you the decimal number.
Describe how to convert a denary number to a binary number.
Write down the place value headers and one by one, under the headers decide whether the number is equal to or more than the header, and based on that, subtract the header from the number and place a 1 under the header or place a 0 if the header is larger than the number. Continue doing this for the rest of the headers.
How can a binary number be converted to hexadecimal?
To convert a binary number to hex, firstly split the binary number into nibbles (a nibble is 4 bits), and using smaller place value headers, convert the nibbles to denary. Then, using the hex number system, convert the denary numbers to hex if needed.
How can you convert a hex number to denary?
Write the hex number and above each hex integer, write the base-16 place values with the smallest at the far right, increasing in multiples of 16 (1, 16, 256…). Then convert any hex digits to denary and multiply the hex digits by the place values, and add these multiplication results to get the denary result.
Describe the method of converting a denary number to hexadecimal.
To convert from decimal to hex, firstly convert the denary number to binary, then split the binary number into two smaller nibbles which will be converted to decimal before converting the decimal numbers (if needed) to hex.
What is a bit?
A bit the smallest and most fundamental piece of information/memory in a computer. A bit can be in the form of either a 1 or 0, used and represented by a high or low current computer.
What is equal to 4 bits?
4 bits = a nibble.