Binary Number System
The Binary number system has a base of 2. Therefore, the 2 digits 0 and 1 are used. This number system is basically the same as the decimal (Base 10) number system except only two digits are used. Binary numbers are made up of binary digits which are referred to as bits. Note: Bit is short for Binary Digit.
Bits are not meaningful on their own typically they will be grouped together. One key grouping is 8 bits together, which is called a byte. A byte can represent 256 values; ranging from 0 to 255.
Note: The origin of the word byte is believed to have been derived by computer scientists making reference to data storage as being "by eight".
Like the decimal system, binary also has a place value or weighting. Each place value or weighting factor is associated with a power of two.
2^{7} | 2^{6} | 2^{5} | 2^{4} | 2^{3} | 2^{2} | 2^{1} | 2^{0} |
---|---|---|---|---|---|---|---|
128's | 64's | 32's | 16's | 8's | 4's | 2's | 1's |
To represent the decimal number 160 in binary would require the eight bit binary number 10100000^{2} (Subscripting the base number to the end of the number helps indicate what base the number is representing, in this case binary). This number as we can see is neither intuitive nor concise. It takes five more digits to represent than the decimal version. However, binary numbers are more natural for digital computers to work with. In a digital computer the digits '1' and '0' can be thought of as 'On' and 'Off', 'True' and 'False' or 'Yes' and 'No'. The reason computers use binary is because the values '0' and '1' can be represented by electricity, e.g. no current = 0, a current = 1.