Why do you use decimal number instead of binary number?

Answer 1

The octal and hexedecimal numbering system allows you to specify the contents of an object with fewer characters, making it easier to read and write the values. An example is 0001001000110100 is 123416 or 110648. It is also 466010 but that requires a non-trivial conversion, something you can not easily do by sight.

Answer 2

The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 is 1001010, which can be grouped into (00)1 001 010 - so the octal representation is 112.

In the decimal system each decimal place is a power of ten. For example:

In the octal system each place is a power of eight. For example:

By performing the calculation above in the familiar decimal system we see why 112 in octal is equal to 64+8+2 = 74 in decimal.

Answer 3

Why does the decimal number system exist?

Or to put it another way, they are just different ways of representing numbers (like the base 4, base 5, base 6, base 13 systems) to the base 10 (or decimal) system that we use in every day life which has probably come about because humans have five digits on two hands giving a total of ten.

However, Octal (base 8) and Hexadecimal (base 16) are useful ways to represent, in concise notation, base 2 (or binary) numbers which digital computers find extremely easy to use as each binary digit (bit) has one of only two values 0 or 1, low voltage or high voltage, etc.

As 8 and 16 are each a power of 2, each octal or hexadecimal digit represents an exact number of binary digits (3 for octal, 4 for hexadecimal), and so conversion between the two is easy for a human.

Although octal numbers use the digits 0-7 and hexadecimal numbers the digits 0-F (with A-F representing the decimal numbers 10-15 which can fit into one hexadecimal digit, or nybble) making them easier to use, they have a problem in that 3 does not divide exactly into 8 (the number of bits in a byte), 16 (bits in 2 bytes), 32 (bits in 4 bytes) or 64 (bits in 8 bytes) which are the usual unit sizes of data that a computer processes, meaning that the most significant octal digit would be limited to 0-1 or 0-3 even though the correct range for octal digits is 0-7; thus it may not be obvious why a program is failing, since the number is a valid octal number. However, but splitting the number up into 4 bit blocks, there is an exact number of whole blocks in bytes, etc and all the bits can be expressed in an exact number of nybbles.

Example (of octal):

The (standard) access protection bits on a *nix system come in sets of three bits. In each set, there is a bit for Read access, one for Write access and one for eXecute access. There are three sets of these protection bits, one for the file owner, one for members of their group and one for every one else.

So each file has 9 access protection bits: rwxrwxrwx which can be present (to allow the action or absent to prevent it).

Protection could be say "rwxr-xr-x" or "rw-r--r--". For the computer these are stored using bits, so these would be stored as the binary numbers "111101101" and "110100100" respectively.

Trying to read those for a human is difficult, however, by splitting them up into blocks of 3 bits they becomes slightly easier to read: "111 101 101" and "110 100 100" as well as splitting out each of the protection blocks.

But these still look large, so converting each set of 3 bits to an octal digit results in "755" and "644" respectively which are not only easier to read (with less likelihood of an error) but also means the human an interpret the protection bits easily - all s/he has to remember is that Read = 4, Write = 2 and eXecute = 1, and adding together the allowed permissions gives the value (eg Read + Write = 4 + 2 = 6) in each digit, with each digit representing a different protection block.

If the numbers were converted to decimal, they would be "493" and "420" which hide the underlying bit patterns.

Hexadecimal could also be used, but even though the bit patterns can be easily worked out, the underlying protection block bit patterns would be hidden (since they use 3 bits): "1ED" and "1A4"

In everyday use we still use sexagesimal (base 60) numbers (which go back to the Babylonians), however we use two decimal digits to represent the 0-59 possibilities for each digit:

For example - time:

1 minute = 60 seconds, 1 hour = 60 minutes.

⇒ the time 5:25:59 is a sexagesimal number using colons to separate the digits.

In decimal this becomes 5 x 602 + 25 x 60 + 59 = 19559 - the number of seconds since midnight. So in reading time, you are actually reading a sexagesimal representation of the second (or minute) of the day!

Answer 4

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Answer 5

Because we learned to count in tens.