Converting to a Binary Pattern In all modern computers memory can either be ON or OFF. On is indicated by 1 and off is indicated by 0. The code will consist of a string of 1’s and 0’s. Each 1 or 0 is called a bit – Binary digit. 

To understand the binary system it is important to think about how the decimal (denary) system works. For example the number 134 represents one hundred, three tens and four ones 

100 10 1 

1      3   4

Moving from left to left each digit is worth ten times the previous one, this is a base ten number system.

However the binary system uses a base two system, therefore as we move from right to left each digit is worth twice as much as the previous one.

Again use the example of 134: 

128 64 32 16 8 4 2 1 

  1   0  0  0  0 1  1   0 

Digital data can be classified using the following units of storage.

Bit   A single 1 or 0

Nibble   4 bits

Byte   8 bits

Kilobyte   1024 bytes

Megabyte   1024 kilobytes

Gigabyte     1024  Megabytes

Terabyte    1024 Gigabytes

Hexadecimal This system is a base 16 number system. To account for all 16 possibilities it uses the digits 0 – 9 and characters A–F. The advantage of this system is that it is easy to convert from binary to hexadecimal and it is easy to read and write down the hexadecimal equivalent of each number. 

To convert between Hexadecimal and Binary, we use the first 4 bits to represent the first value in the Hex code and the last 4 bits to represent the second number in the HEX code. To convert between Hex and binary we simply reverse the process.

Binary addition is an easy calculation to perform and very similar to how decimal numbers are added together. Two numbers are lined up; one under the other, then starting from the right add each column, recording the result and carry as you go along. There are 4 possibilities when adding:

0+0 = 0 

0+1 = 1 

1+1 = 2 which is 10 in binary, 

1+1+1 (carried over) = 3 which is 11 in binary, which is 1 with a carry of 1

When performing binary addition if the answer of the addition is greater than 255, then we cannot represent that number using 8 bits. This is caused an overflow error and we will need 9 bits to represent the answer accurately.