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Number Systems

• The "mother tongue" of computers are neither digits nor letters. Everything you write and see is translated to the binary number system. So the "mother tongue" of computers are the digits one and zero.

Decimal Number System - Base 10

• A number system that uses ten digits: 0 - 9.

• These digits are readable and are commonly used in real life.

Binary Number System - Base 2

• A number system that uses two digits: binary digits, it means 0 and 1. 

• The binary number system can be easily implemented in electonics and computer systems. 0 and 1 can also be expressed as on and off. An electric pulse either exists or does not exist. If we used the decimal number system, we would have to use 10 different electric pulses which would make data saving and computer architecture more complicated .

• All characters and other data can be easily encoded to binary numbers.

Hexadecimal Number System - Base 16

• A number system that uses 16 characters: digits 0 - 9 and letters A - F.

• Easy and often used in addressing and computer systems where Bytes are used - 8-bit, 16-bit, 32-bit, 64-bit or 128-bit determination. This is most frequently used for memory addressing, bus width or for other purposes. There are two important purposes for use - for programming and memory usage diagnostics. Example: usage of a memory block named D9000000 - D9003FFF is more readable than:

3640655872 - 3640672255 (Decimal)

11011001000000000000000000000000 - 11011001000000000011111111111111 (Binary)

• Space saving - If we take into account the arrangement of particular characters by Bytes, the number D9000000 takes 8 Bytes and the number 3640655872 takes 10 Bbytes. If we write the same in the binary code, it will take 34 Bytes when one byte is one digit. If the number is written in the binary code when one bite is one digit, the number will have 4 Bytes and 2 bits (5 Bytes or 34 bits). 

• For distinguishing hexadecimal numbers there is the letter h (e. g. 25Ah) or the symbol 0x (e. g. 0x25A) used.

• Octal Number System - a system that uses digits 0 - 7, is similar to the hexadecimal number system .

Table of Conversion from the Binary to the Decimal Number System

• Example - 10110001 - 1+0+0+0+16+32+0+128 - 177 (B1) 

• For those who do want to calculate the conversions - Windows calculator will make it (but you have to switch to sience mode)

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