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Aqa As Computer Science Paper 2 Latest Update Study Set N Natural numbers, positive whole numbers and zero. Set Z Integers, positive and negative Set Q Quotients, Rational numbers, can be expressed as a ratio between two integer Irrational numbers Cannot be expressed as a ratio between 2 n...

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  • September 22, 2024
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Aqa As Computer
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Study
Set N
Natural numbers, positive whole numbers and zero.
Set Z
Integers, positive and negative
Set Q
Quotients, Rational numbers, can be expressed as a ratio between two integer

,Irrational numbers
Cannot be expressed as a ratio between 2 numbers, root 2, pi
Real numbers
Set of irrational numbers, Q, Z, N
Ordinal numbers
Integers used to describe numerical position of objects. First, second, third
Counting and measuring
Natural numbers for counting, real numbers for measuring
Decimal
base 10, used by humans, subscript 10, also called denary, 0-9
Binary
base 2, used by computers as they represent high or low voltage, 0 or 1, subscript 2
Hexadecimal
base 16, used as shorthand representation for binary, 0-9 followed by A-F,
subscript 16
Decimal Prefixes
What is a bit
Binary digit, can be 1 or 0
What is a byte
8 bits
Name of 4 bits
Nibble
Notation of bit and byte?
Bit is lower b, byte is upper B
How many different values can be represented with n bits
2^n

, Signed vs unsigned
Unsigned binary numbers can only represent positive numbers, signed can
represent negative
Range of unsigned number
0 to (2^n)-1
Addition of unsigned binary rules
Multiplication of unsigned
Like short multiplication/addition
Two's complement
Allows for representation of negative numbers, most significant bit is negative
Subtraction
When computers subtract, they add negative numbers. Works the same, result can
be read off
Range of two's complement number
2^(n -1)-1 to -2^(n-1)
Fixed point binary
Specific number of bits are placed before and after the point, Bits after are valued
at 1/2, 1/4, 1/8 etc.
Floating point binary (binary to decimal)
Represented in two's complement. Binary point between first and second number,
moved to the right number specified by exponent. Then treat as fixed point binary.
Floating point binary (decimal to binary)
Convert to fixed point. make it begin with 01 if positive, 10 if negative. Binary
point is assumed to be between first and second digit. Move digit and turn
exponent into binary.
Rounding errors with floats
Some decimal numbers can't be represented exactly in binary, such as 1/3

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