History and Bases – Why do humans use the decimal number system? Why do computers use the binary number system? Why do programmers use the hexadecimal number system?
The decimal number system is based on ten fingers (aka digits). This is how we first started counting. Today it is primarily used for money purposes. It is based on the symbols 0, 1, 2, 3, 4, 5, 6, 7 , 8, and 9. After that all digits are just repeated.
The binary number system was chosen due to the fact that it was much more economical to program two position switches due to the invention of the transistor. The binary number system is based on two symbols (0 and 1).
The hexadecimal number system is based on sixteen symbols. The sixteen symbols chosen by programmers were 0 through 9 and A, B, C, D, E, and F. These are the symbols that would be show in a “hex dump” or the Blue Screen of Death (BSOD). These symbols also appear in the hexadecimal colour code and the Internet’s IP addresses.
The Place Value Method (see attached PDF for review) USED WHEN: Converting from ANY number system into the decimal number system. (ie. Binary to Decimal OR Hexadecimal to Decimal)