1.1 Number systems

Why do computers use binary?

Any form of data needs to be converted to binary to be used by a computer

Computers process data using switches or logic gates

These only use 2 states, on or off, 1 or 0

This is then stored in registers

Binary is base…

2

Hexadecimal is base…

16

Denary is base…

10

Area in Computer Science where hexadecimal is used

URLs

MAC addresses

Colour codes

Benefits of hexadecimal

Can represent 16 bit words as only 4 hexadecimal digits

Easy to convert back to binary if necessary

Overflow error

Value is greater than 255 in an 8 bit register

Computer has a predefined limit that it can represent or store for example 16 bit

If a value outside this limit is returned an overflow error happens

Most significant bit

The bit with the highest value

Least Significant Bit

The bit with the lowest value

In two’s compliment what is the value of the most significant bit

Negative

How to do two’s compliment method?

Write positive number in binary

Invert all the bits

Add one

Why may programmers use hexadecimal?

Quicker to write and read

Takes up less space of the screen

Quicker and easier to debug

Less likely to make a mistake