CS unit 3 Notes(theory)
Number systems:
Natural numbers – positive whole numbers used for counting
Integer number – positive or negative whole number
Rational number – number that may be expressed as ratio or fraction
Real number – any possible real-world quantity expressed as a number. Does
not include numbers such as positions
Ordinal numbers- number used to describe numerical positions e.g., 4th.
Irrational numbers - cannot be written as fractions or ratios.
Denary- base 10 number system going from 0-9
Binary- base 2 number system going from 0-1
Hex – base 16 number system going from 0-9 and then A-F(A = 10, F = 15)
Binary-hex conversion:
If number in denary convert to binary
1. split binary number into equal bits of 4.
2. Find the denary of the split binary numbers. This means the max denary
can only be 15 which is F.
3. This means that a byte (8 bits) Is only 2 values
e.g., conversion of 179:
1. 179 = 10110011
2. split = 1011 and 0011
3. 1011 = B 0011 = 3 therefore conversion is B3
Reverse process for hex to binary:
B in denary is 11. Convert 11 to binary and convert 3. This gives binary.
Hex is preferred as it is easier to remember than binary, and it is easier to read
through for humans. Can be used for defining colours
Note: To prove if number is hex convert each number to denary and starting
from the right multiply each by a power of 16n where n starts of as 0 for the
first denary number and 1 is added each time
, Overflow error- when the result of an addition is too large for the number of
bits the computer with
Bits bytes and binary:
Binary for A = 65
Bit- a single component that can be 1 or 0.
A byte is 8 bits
To calculate the number of different combinations of bits, we use the
expression 2n where n is the number of bits. E.g., with 3 bits the number of
combinations are 8.
2n -1 – highest possible denary number
Binary:
Name Symbol Power Value
Kibi byte KIB 210 1,024
Mebi byte MIB 220 1,048,576
Gibi byte GIB 230 1,073,741,824
Tebi byte TIB 240 1,99,511,627,776
Decimal:
Name Symbol power value
Kilo byte K 103 1,000
Mega byte M 106 1,000,000
Giga byte G 109 1,000,000,000
Tera byte T 1012 1,000,000,000,000
ASCII: represents all lower and uppercase letters in English alphabet in a byte.
This means there are 28 possible combinations.
Unicode: Like ASCII but has 16 bits instead of 8. This means it can represent 216
different combinations. Adv: can represent more combinations (e.g., other
languages) Disadv: takes up more space per character
Number systems:
Natural numbers – positive whole numbers used for counting
Integer number – positive or negative whole number
Rational number – number that may be expressed as ratio or fraction
Real number – any possible real-world quantity expressed as a number. Does
not include numbers such as positions
Ordinal numbers- number used to describe numerical positions e.g., 4th.
Irrational numbers - cannot be written as fractions or ratios.
Denary- base 10 number system going from 0-9
Binary- base 2 number system going from 0-1
Hex – base 16 number system going from 0-9 and then A-F(A = 10, F = 15)
Binary-hex conversion:
If number in denary convert to binary
1. split binary number into equal bits of 4.
2. Find the denary of the split binary numbers. This means the max denary
can only be 15 which is F.
3. This means that a byte (8 bits) Is only 2 values
e.g., conversion of 179:
1. 179 = 10110011
2. split = 1011 and 0011
3. 1011 = B 0011 = 3 therefore conversion is B3
Reverse process for hex to binary:
B in denary is 11. Convert 11 to binary and convert 3. This gives binary.
Hex is preferred as it is easier to remember than binary, and it is easier to read
through for humans. Can be used for defining colours
Note: To prove if number is hex convert each number to denary and starting
from the right multiply each by a power of 16n where n starts of as 0 for the
first denary number and 1 is added each time
, Overflow error- when the result of an addition is too large for the number of
bits the computer with
Bits bytes and binary:
Binary for A = 65
Bit- a single component that can be 1 or 0.
A byte is 8 bits
To calculate the number of different combinations of bits, we use the
expression 2n where n is the number of bits. E.g., with 3 bits the number of
combinations are 8.
2n -1 – highest possible denary number
Binary:
Name Symbol Power Value
Kibi byte KIB 210 1,024
Mebi byte MIB 220 1,048,576
Gibi byte GIB 230 1,073,741,824
Tebi byte TIB 240 1,99,511,627,776
Decimal:
Name Symbol power value
Kilo byte K 103 1,000
Mega byte M 106 1,000,000
Giga byte G 109 1,000,000,000
Tera byte T 1012 1,000,000,000,000
ASCII: represents all lower and uppercase letters in English alphabet in a byte.
This means there are 28 possible combinations.
Unicode: Like ASCII but has 16 bits instead of 8. This means it can represent 216
different combinations. Adv: can represent more combinations (e.g., other
languages) Disadv: takes up more space per character
