Maths

Maths Topics

• order of operations
• algebra
• linear equations
• quadratic equations
• simultaneous equations
• binary
• hexadecimal
• octal
• Boolean algebra
• logic gates
• probability
• statistics

Binary

Binary is a number system composed of two digits: 0 and 1. This means every number has to be represented using a combination of these digits:

0 in decimal is also 0 in binary.
1 in decimal is also 1 in binary.
2 in decimal, however, is 10 in binary.

Converting from binary to decimal

To convert from binary to decimal, list the powers of two in reverse for each digit of the binary. For example:

 1  1 1 1 1 1
32 16 8 4 2 1

This means 111111 in binary is 32 + 16 + 8 + 4 + 2 + 1 = 63.
If one of the digits is 0, it is simply excluded from the addition:

 1  0 1 1 0 1
32 16 8 4 2 1

Therefore 101101 is 32 + 8 + 4 + 1 = 45.

Converting from decimal to binary

To convert from decimal to binary, divide the number by two, write down the answer, set aside the remainder and repeat. For example, to work out the binary for the decimal 45:

45 / 2 = 22 remainder 1
22 / 2 = 11 remainder 0
11 / 2 = 5 remainder 1
5 / 2 = 2 remainder 1
2 / 2 = 1 remainder 0
1 / 2 = 0 remainder 1

The binary is the value of the remainders in reverse order: 101101.

Lauren's blog has some helpful diagrams on this topic.

Hexadecimal

Hexadecimal is a base 16 number system. This means it uses 16 different characters to express the values of numbers. These characters are: 0123456789ABCDEF. A in hexadecimal is 10 in decimal or "base 10", which is the number system we are used to.

One great thing about hexadecimal is the easy conversion to and from binary. You simply convert each character at a time to four binary digits, unlike decimal where you have to break down the whole number. Here's an example:

1 = 0001
2 = 0010
9 = 1001
A = 1010
F = 1111

129AF = 00010010100110101111