APPENDIX C

Decimal, binary and hexadecimal numbers

Homosapiens are used to Decimal numbers, i.e. 0,1,2,3 …… 9. Electronic machines or chips use Binary numbers 0 and 1, (OFF and ON).

Decimal numbers increase in tens, i.e. 267 means 7 ones, 6 tens and 2 hundreds.

Binary numbers increase in twos, i.e. 1010. The right hand 0 means no ones, the next digit means 1 two, the next means no fours, the next 1 eight etc.

The binary number 1010 consists of 4 BInary digiTs it is called a 4 BIT number. 1010 is equivalent to 10 in decimal numbers.

We can change decimal numbers to binary and binary numbers to decimal. Digital systems, i.e. Computers are a little better than we are at this.

Consider the decimal number 89, to turn this into a binary number write the binary scale:

128 64 32 16 8 4 2 1

To make 89 we need (0 × 128) + (1 × 64) + (0 × 32) + (1 × 16) + (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1).

So 89 in decimal = 01011001 in binary.

To convert a binary number to decimal add up the various multiples of 2, i.e. 10011010 is:

A long string of binary numbers is difficult to read, i.e. 11010101 to make this shorter and therefore easier to put into a microcontroller Hexadecimal numbers are used. Hexadecimal numbers increase in sixteen's and are described by sixteen digits. Table C.1 shows these 16 digits and their decimal and binary equivalents.

Table C.1 4 BIT Decimal, binary and hexadecimal representation

The PIC microcontrollers are 8 bit micros, they use 8 binary digits for number representation like

10010101 this is

The largest decimal number that can be represented by an 8 bit number is:

11111111 which represents:-

But we can program our microcontroller to increase our number representation from 8 bits i.e. up to 255:

to 16 bits, numbers up to 65,535

to 24 bits, numbers up to 16,777,215

to 32 bits, numbers up to 4,294,967,295 etc.

As mentioned earlier hexadecimal numbers are a shorter way of writing binary numbers. To do this divide the binary number into groups of 4 and write each group of 4 as a hex number.

i.e. 10010110 as 1001 0110 in binary

= 9 6 in hex.

i.e. 11011010 as 1101 1010 in binary

= D A in hex.

Table C.2 shows some of the 255 numbers represented by 8 bits.

Table C.2 8 BIT Decimal, binary and hexadecimal representation