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What is the importance of an octal number?
Why do we use Octal? Octal comes into a close second. In octal, you can represent, at most, 3 bits with a single octal digit. So it's very easy to say 311 is 11 001 001. The problem with octal, as you can see, is that the 3rd octal digit can only goes as high as 3, so it does not represent a byte as cleanly as hex. Octal is used in Unix for permissions due to its 3-bit nature. If we take the three specific entitlements (read, write, execute) for a file, we find that it coincides very well with octal. That's why you see those really funky "chmod 744" commands, because they are octal representation of permissions, 111 100 100, or R-W-E, Read, Read for owner, group, world respectively (at least that is how it was explained to me). The leftmost bit represents the read flag, the middle one represents the write flag, and the rightmost flag represents execute. So if you wanted the permission for read-write, it would be 110, or 6. Read and execute would be 101 or 5. Additional Answer: Since Octal (base-8) and Hexadecimal (base-16) are powers of two, that means they map directly to binary. For instance, each character in a base-16 number corresponds to 4 bits. So if I have a 4-byte (32-bit) number in hex, I could write out the binary sequence without really thinking about it. Also, one digit could change, and it would only change those corresponding 4 bits. In decimal, changing one digit can change many or all of the bits. This is why it is easier for programmers to use Hex, because it is a direct representation of the binary sequence. I believe we adopted the decimal system because we have 10 fingers. In actuality, hexadecimal would be a much better system for everyone to use. Society as a whole would be more mathematically inclined if they began learning hex when they were children, and we just did away with decimal altogether. Hexadecimal is much more natural than decimal. Octal and hexadecimal numeration systems would be pointless if not for their ability to be easily converted to and from binary notation. Their primary purpose in being is to serve as a "shorthand" method of denoting a number represented electronically in binary form. Because the bases of octal (eight) and hexadecimal (sixteen) are even multiples of binary's base (two), binary bits can be grouped together and directly converted to or from their respective octal or hexadecimal digits. With octal, the binary bits are grouped in three's (because 23 = 8), and with hexadecimal, the binary bits are grouped in four's (because 24 = 16). Incidentally, hexadecimal notation is more popular, because binary bit groupings in digital equipment are commonly multiples of eight (8, 16, 32, 64, and 128 bit), which are also multiples of 4. Octal, being based on binary bit groups of 3, doesn't work out evenly with those common bit group sizing's.
Why are octal or hexadecimal number systems used as shortcut notations?
With computers it is often bit (binary digit) patterns that matter and with octal or hexadecimal numbers it is easy to convert them to binary as each digit is represented by an exact number of binary digits (3 for octal, 4 for hexadecimal) without any waste.Using *nix access permissions as an example, the basic permissions are split into 3 groups (Owner, Group, World), each with 3 possible permissions (Read, Write and eXecute). These are stored as a bit pattern: if set the permission is granted, if not set permission is not granted. A file with rwxr-x--x (rwx for owner, r-x for group and --x for world) is stored in binary as 111101001 which can be represented in octal easily by reading it in groups of 3 bits: 111101001 → 111 101 001 = 0751, or in hexadecimal by splitting it into groups of 4 bits: 111101001 → 1 1110 1001 = 0x1e9; but to convert it to decimal requires: 256 + 128 + 64 + 32 + 8 + 1 = 489.Similarly, going the other way: what permissions are represented by 420?420 to binary:420 ÷ 2 = 210 r 0210 ÷ 2 = 105 r 0105 ÷ 2 = 52 r 152 ÷ 2 = 26 r 026 ÷ 2 = 13 r 013 ÷ 2 = 6 r 16 ÷ 2 = 3 r 03 ÷ 2 = 1 r 11 ÷ 2 = 0 r 1→ 420 = 110100100 in binary = rw-r--r--420 in octal is 0644 and in hexadecimal is 0x1a40644 to binary: 110 100 100 → 110100100 as before [much quicker and easier]0x1a4 to binary: 1 1010 0100 → 110100100 again.
The binary number 11 would have a decimal equivalent of 11?
this isn't the fact that the binary number 11 will have decimal equivalent 11... instead it have decimal number 1011 for decimal equivalant 11.here is the alogorithms for converting the decimal number to binary equivalent...!!!#include#includevoid main(){ int i,n,j,b[100];clrscr();printf("Enter a Number:");scanf("%d",&n);i=0;while(n>0){b[i]=n%2;n=n/2;i++;}printf("\n\nBinary Equivalent:");j=i-1;for(i=j;j>=0;j--)printf("%d",b[j]);getch();}using this algorithms... the binary equivalent of any number is taken out...!!! enjoy... have any query... email at :- "devilllcreature@yahoo.com" thank you....!!!
What is the equivalent of binary number 100 in base 10?
100 in base two equals 4 in base 10 1*(2^2)+0*(2^1)+0*(2^0)=2^2=4
What is 101 101 in binary?
55. 101 in binary is 5. there is a shortcut in getting the equivalent in binary. 421 if it is 1, then it's 001. if it is 2, then it's 010. if it is 3, then it's 011. if it is 4, then it's 100. if it is 5, then it's 101. see? you just have to add the numbers that you need. you'll write 1 when you used the number that is needed and 0 when not.
