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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.
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.
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!
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What is the advantages of binary digits over the decimal?
Computers do not understand decimal notation. All information (both instructions and data) must be converted to a binary representation before the machine can understand it. We use the symbols 0 and 1 (binary notation) but the machine has a variety of physical representations it can use to encode binary data, including transistors, flux transitions, on/off switches and so on.
What is the 4-binary number assoiated with the hexadecimal symbol C?
0xc = 1100 Hexadecimal digits use exactly 4 binary digits (bits). The 0x0 to 0xf of hexadecimal map to 0000 to 1111 of binary. Thinking of the hexadecimal digits as decimal numbers, ie 0x0 to 0x9 are 0 to 9 and 0xa to 0xf are 10 to 15, helps with the conversion to binary: 0xc is 12 decimal which is 8 + 4 → 1100 in [4 bit] binary.
How are the base 16 and base 2 numbers related?
Both base 16 and base 2 number systems use binary numbers (1 and 0) to write out and define decimal numbers.
What is radix in number system?
The radix refers to the base of a number system: the total number of possible digits. The decimal number system that we all use is base ten, as it has ten distinct digits (0,1,2,3,4,5,6,7,8,9). Commonly used bases in computing include binary, octal, and hexadecimal, which have two, eight, and sixteen digits, respectively.
10011 is the binary number system way of writing?
The binary number 10011 is equivalent to the decimal number 19 in the base-10 number system. In binary, each digit represents a power of 2, starting from the right with 2^0, 2^1, 2^2, and so on. Therefore, 12^4 + 02^3 + 02^2 + 12^1 + 1*2^0 = 16 + 0 + 0 + 2 + 1 = 19.
What is the advantage of having the binary number system to represent data inside the computer instead of the decimal number system?
They use the binary sysem because the number 1 means the switch is turned on and the number 0 means the switch is off. There is no way to use the decimal number system.
What is the binary number of 63?
If you use Windows, you can use the Windows calculator to convert from decimal to binary. Change to scientific mode, be sure the calculator is in decimal, type the decimal number, and switch to binary. If you are practicing decimal to binary conversion, this is a great tool to verify that you have done your calculations correctly.
What decimal number is equivalent to binary number 121?
That's not a binary number ! Binary numbers can only use the digits 1 and 0.
Which is the following represents the binary equivalent of the decimal number 23?
The binary equivalent of the decimal number 23 is 10111. You can use an online converter to easily find this solution.
What is the binary number of decimal number of 24?
To convert decimal to binary, and binary to decimal, you can use the calculator included in Windows. Up to Windows XP, select "scientific" mode; in Windows 7, select "programmer" mode. <><><><><> 2410 = 110002.
Do computers use the decimal number system to store data?
No, they use the binary system
Why domcomputers use binary number system instead of decimal number system?
Because it's much, much easier to design electronic two-way switches that electronic ten-way switches. A two-way switch leads to binary.
How do you convert Binary-to-Decimal and Decimal-to-Binary?
You can use a table to convert binary to decimal & back:MSBBinary DigitLSB2827262524232221202561286432168421Figure out the greatest power that will fit into the number you want to convert to binary. Move to the next lower power of two. If you can fit into the next lower number write down a "1", if it can't put down "0". Put together the binary answer.
Could the binary number 1000 be a binary coded decimal?
It's 8. (Next time you can use calc.exe of your windows.)
How many digits are there in the binary equivalent of 56?
56 in binary is 111000. Unlike the decimal number system where we use the digits.
Why do computers use the decimal system?
Computers use a binary system, not decimal.
What is the binary number of 209.85.153.94?
Just use the Windows calculator, and set it to scientific mode, or use any scientific calculator that supports binary/decimal. In the Windows calculator, make sure you are in decimal, type in each of the four numbers, then select "Binary" to convert to binary. You will have to fill out some of the binary numbers with zeroes to the left (each one must have 8 binary digits).Just use the Windows calculator, and set it to scientific mode, or use any scientific calculator that supports binary/decimal. In the Windows calculator, make sure you are in decimal, type in each of the four numbers, then select "Binary" to convert to binary. You will have to fill out some of the binary numbers with zeroes to the left (each one must have 8 binary digits).Just use the Windows calculator, and set it to scientific mode, or use any scientific calculator that supports binary/decimal. In the Windows calculator, make sure you are in decimal, type in each of the four numbers, then select "Binary" to convert to binary. You will have to fill out some of the binary numbers with zeroes to the left (each one must have 8 binary digits).Just use the Windows calculator, and set it to scientific mode, or use any scientific calculator that supports binary/decimal. In the Windows calculator, make sure you are in decimal, type in each of the four numbers, then select "Binary" to convert to binary. You will have to fill out some of the binary numbers with zeroes to the left (each one must have 8 binary digits).
