Theory: Data Rep Flashcards
List and define each number system
-N is natural numbers or Z+, positive integers
-Z is all integers, positive and negative
-Q is all rational numbers, numbers that can be represented as a proper/improper fraction Q = {a/b|a,b ∈ Z , b != 0}
-R is the set of real numbers, all rational and irrational numbers, algebraic numbers
-C is complex or imaginary numbers. C ={ a+bi| a,b ∈ R , b != 0}
What set of numbers is used to describe the location of a number relative to another number?
Ordinal numbers
Which number base is used by humans for counting?
Base 10/decimal/denary
Which number base can be denoted with a subscript 16?
Hexadecimal
What is the decimal equivalent of the hexadecimal digit E?
14
Which number base is useful as a shorthand representation for binary?
Hexadecimal
What is the decimal equivalent of the binary number 0101?
5
What is the binary equivalent of the hexadecimal number A3?
10100011
What is the binary equivalent of the decimal number 14?
1110
Describe what is meant by a bit
A bit is the smallest and fundamental unit of information which can either take the value 1 or 0
How many bits are there in a byte?
8
How many bits are there in a nybble?
4
How many nybbles are there in a byte?
2
How many values can be represented with 4 bits?
16, 0-15
How many values can be represented with 20 bits?
2^20= 1048576, 0-1048575
How many bytes are there in a mebibit
2^20 = 1048576
How many bytes in a kibibyte?
2^10= 1024
Describe the uses of hexadecimals.
-third most commonly used number system, large values can be represented using fewer characters. Also easier to interpret than binary.
-colour values
-mac addresses
List the names for bit values and how many bits they represent.
-bit: smallest value, one digit
-nibble: four bits
-byte: eight bits
-(kibibyte
-
In binary multiplication, what are the respective names for the number being multiplied and what it’s being multiplied by?
-multiplicand and multiplier
Describe the concept of two’s complement
Binary numbers beginning with 1 are negative numbers, those beginning with 0 are positive
The range of possible values that can be represented:
Define the Caeser cypher and Polyalphabetic encryption.
A caeser cypher uses a given numerical key eg. 4 and each letter in a message is shifted along the alphabet by that number. Eg A becomes E.
When used with Polyalphabetic encryption, each letter of the message uses a different key.
Is 0 included in the set of natural numbers?
Yes
Every natural number greater than 1 can be written as a product of what?
Prime numbers