Integers
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From: David McGlone on 30 Jun 2010 22:02 Hi again I'm trying to learn about octal numbers and I don't understand this: Binary: 001000101111 breakdown: (001)= 1 (000)= 0 (101)=5 (111)=7 I know it's similar to unix permissions, but I'm not understanding where for example: 111 = 7 wikipedia has got me all confused. -- Blessings, David M.
From: Stephen on 30 Jun 2010 22:12 On 10-06-30 10:02 PM, David McGlone wrote: > Hi again > > I'm trying to learn about octal numbers and I don't understand this: > > Binary: 001000101111 > breakdown: (001)= 1 (000)= 0 (101)=5 (111)=7 > > I know it's similar to unix permissions, but I'm not understanding where for > example: 111 = 7 > In base 10, which you use every day, we go 0 1 2 3 4 5 6 7 8 9 10 The number 10 is the number of distinct digits we use. In binary we only us two, 0 and 1, so 10 is 2 decimal So we go 0 = 0 decimal 1 = 1 << important 10 = 2 << important 11 = 3 100 = 4 << important 101 = 5 110 = 6 111 = 7 So binary 111 is 4 + 2 + 1 = 7 Stephen
From: Shreyas Agasthya on 1 Jul 2010 03:59 It would also mean that 7 (8 digits which includes 0) is the highest numeric representation that you can have or go up to in an octal representation. So to take your example and represent an octal number : 001000101111 (subscript 2) = 1057(subscript 8) --Shreyas On Thu, Jul 1, 2010 at 7:42 AM, Stephen <stephen-d(a)rogers.com> wrote: > On 10-06-30 10:02 PM, David McGlone wrote: > >> Hi again >> >> I'm trying to learn about octal numbers and I don't understand this: >> >> Binary: 001000101111 >> breakdown: (001)= 1 (000)= 0 (101)=5 (111)=7 >> >> I know it's similar to unix permissions, but I'm not understanding where >> for >> example: 111 = 7 >> >> > In base 10, which you use every day, we go > 0 > 1 > 2 > 3 > 4 > 5 > 6 > 7 > 8 > 9 > 10 > > The number 10 is the number of distinct digits we use. > > In binary we only us two, 0 and 1, so 10 is 2 decimal > > So we go > > 0 = 0 decimal > 1 = 1 << important > 10 = 2 << important > 11 = 3 > 100 = 4 << important > 101 = 5 > 110 = 6 > 111 = 7 > > So binary 111 is 4 + 2 + 1 = 7 > > Stephen > > > -- > PHP General Mailing List (http://www.php.net/) > To unsubscribe, visit: http://www.php.net/unsub.php > > -- Regards, Shreyas Agasthya
From: tedd on 1 Jul 2010 11:33 At 10:02 PM -0400 6/30/10, David McGlone wrote: >Hi again > >I'm trying to learn about octal numbers and I don't understand this: > >Binary: 001000101111 >breakdown: (001)= 1 (000)= 0 (101)=5 (111)=7 > >I know it's similar to unix permissions, but I'm not understanding where for >example: 111 = 7 > >wikipedia has got me all confused. > >-- >Blessings, >David M. David: You're mixing things (Octal/Permissions)-- let's deal with Octal first. All number systems have a defined base for the power of their placeholder. Our Decimal system is based upon tens. More explicitly -- each placeholder in the Decimal system is dependant on a power of ten. For example, the number 559 (DEC) is simply: (5 x 10^2) + (5 x 10^1) + (9 x 10^0) That's 5 times 10 to the power of two, plus 5 times 10 to the power of 1, plus 9 times ten to the power of zero (which is always 1). The sum of the products is 559. I won't go into the reasons why we want to convert numbers between bases, but there are reasons. The beauty of Octal (base 8) is it is much easier to convert from Binary than it is to convert Binary to Decimal. Additionally, it's simpler to convert Octal to Decimal than it is to convert Binary to Decimal, Lastly, it is much easier to take the conversion from Binary to Octal and then convert from Octal to Decimal in a two step process than it is to it all at once by converting Binary to Decimal. That's the main reason why we use Octal. For example: If you take the Binary number: 001000101111 (BIN) and translate that to Octal, you have: 1057 (OCT) How did I do that? That is (as you said above) a very easy process -- you just break it up into groups of three. (100) = 1, (000) = 0, (101) = 5, (111) = 7 But what you are actually doing is: 1 x 10^3 (OCT) + 0 x 10^2 (OCT) + 5 x 10^1 (OCT) + 7 x 1 x 10^0( OCT) -- side note -- Why is 111 = 7? It's because: 1 x 10^2 = 4 1 x 10^1 = 2 1 x 10^0 = 1 Total 7 -- Interestingly enough it's 7 in both Octal and Decimal (and anything greater than base 8). -- end of side note --- But realize the number 10 in Octal is 8 in Decimal. As such, I can convert Octal to Decimal pretty easily by: 1 x 8^3 = 512 0 x 8^2 = 0 5 x 8^1 = 40 7 x 8^0 = 7 559 (DEC) Please note 4 computations. Whereas, if I tried to convert Binary (base 2) directly to Decimal (based 10) it would go like this: 0010 0010 1111 (BIN) 1 x 10^9 = 512 0 x 10^8 = 0 0 x 10^7 = 0 0 x 10^6 = 0 1 x 10^5 = 32 0 x 10^4 = 0 1 x 10^3 = 8 1 x 10^2 = 4 1 x 10^1 = 2 1 x 10^0 = 1 Total: 559 Please note 10 computations! As you can see above, it is *much* easier to take a Binary number and break it into Octal portions by simply looking at the pairs of three, namely: (100) = 1, (000) = 0, (101) = 5, (111) = 7 And from that run the Octal to Decimal conversion. === Now permissions === Permissions are set to the power of 8 (Octal). Why? Because we don't need a higher base number system to cover the needs of setting permissions. It is defined as: read (r) = 4 write (w) = 2 execute (x) = 1 So, the numbers mean: 7 = rwx (read write execute) 6 = rw- (read and write) 5 = r-x (read and execute) 4 = r-- (read) 3 = -wx (write and execute) 2 = -w- (write) 1 = --x (execute 0 = --- (no access) The permission system for files/directories is divided into divisions, namely "Owner", "Group", and "ALL". Each division can have their own permission settings. The standard is to list them in order of "Owner", "Group", and "ALL" such as: 777 means that all three divisions have their permission set to read, write, and execute. 755 means that the Owner has permission set to read, write, and execute whereas the "Group", and "ALL" have their permissions set to only read and execute. You often see this displayed as: Owner Group All example --- chmod 777 rwx rwx rwx rwx rwx rwx Owner Group All example --- chmod 755 rwx r-x r-x rwx r-x -r-x Owner Group All example --- chmod 766 rwx rw- rw- rwx rw- rw- Owner Group All example --- chmod 644 rw- r-- r-- rw- r-- -r-- Owner Group All example --- chmod 600 rw- --- --- rw- --- --- There is no magical rule why we use Octal for this. In fact, we could have used any system greater than base 8 -- even base 16 (HEX), but there was no need for more (there is, but I don't want to explain that). I hope this lifts some of the confusion. Cheers, tedd -- ------- http://sperling.com http://ancientstones.com http://earthstones.com
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