On Wed, 30 Aug 2006, aliensrcooluk at yahoo.co.uk wrote: To write down integers, perhaps? Hex is nice if your bits come in multiples of 4; octal is nice if your bits come in multiples of 3. People on this list claim to have computers with 12, 18, 24, 36, and 48 bit registers, IIRC. Alexey

On 8/31/06, aliensrcooluk at yahoo.co.uk <aliensrcooluk at yahoo.co.uk> wrote: In some contexts, it can make some patterns more apparent than using decimal or hex. One example is the PDP-11 instruction set - if you look at the way the register selection and addressing modes are specified, it's much clearer when you view the instructions in octal rather than hex, even though it's a 16-bit machine. (cf - http://en.wikipedia.org/wiki/PDP-11 and http://www.village.org/pdp11/faq.pages/PDPinst.html ) In binary, many instructions are of the form "biiissssssdddddd", where 'b' is byte vs word, 'iii' is the operand (instruction type), 'ssssss' is the source operand, and 'dddddd' is the destination operand. In octal, it would be represented as 6 digits (000000- 177777) and you can think of the instructions more like 'BISSDD' where 'B' is still byte vs word, 'I' is a single octal digit for the operand, and 'SS' and 'DD' are the source and destination as two octal digits - one being the addressing mode type, the other the register to apply the addressing mode to. As you can see, it's not tough to look at, say, a MOV instruction and see what it does... 010304 copies the contents of R3 to R4. In hex, that would be 0x40C4 and not at all obvious what it's doing at first glance. There are other applications, such as using 7-segment displays where it might be easier to represent things in octal than hex or decimal. It's just another number base, but not as commonly used anymore as hex. -ethan | | | : | : | | | Op | Source | Dest |

Just as hex is appropriate whenever you have bits naturally occurring in groups of four, octal is appropriate whenever you ahve bits naturally occurring in groups of three. Examples that come to mind immediately include PDP-11 (and to a lesser extent 8080) machine languages, any machine whose word size is a multiple of three bits (eg, 12- or 36-bit machines), and Unix file permission bitmasks. /~\ The ASCII der Mouse \ / Ribbon Campaign X Against HTML mouse at rodents.montreal.qc.ca / \ Email! 7D C8 61 52 5D E7 2D 39 4E F1 31 3E E8 B3 27 4B

And on many of my HP calculators. Here goes... As I am sure you know, octal is simply base 8 notation. And (most) computers use a binary code internally. The problem with binary for humans, though, is the long strings of digits that are involved -- think of writing down 32 0's and 1's for a longoword, and being sure you've not missed one, or got them in the wrong order. Now, since 8 is a power of 2 (=2^3), it's very easy to convert between octal and binary. You know how to convert a binary number to hex, right, by spliting the digits up into groups of 4 and converting each block of 4 bitd to hex. Well, you can do the same to convert a binary number to octal, just split the digits up in groups of 3. For example, consider 10101111. To conver to hex, split it up into 4 bit groups 1010 1111 Convert each group 1010 -> A 1111 -> F So the hex equivalent is AF Now to convert it into octal, split it into groups of 3 bits 10 101 111 Convert each group 10 -> 2 101 -> 5 111 -> 7 So it's 257 in octal. Advantage of octal (over hex) include : You only need the digits 0-7. At one time there was considerable resistance to using letters as digits, a second-hand book I bought last week thinkks it's most unsatisfactory to do this. Some machine codes (PDP8, PDP11, and to a lesser extent 8080) are easier for humas to decode if written in octal. For example, the PDP11 instruction to copy R1 into R2 is (IIRC) 010102 in octal. You can decode that by hand -- from the left 01 -> It's a move 0 -> Source addressing mode = register (not indirect or indexed, or...) 1 -> Source register = R1 0 -> Destination addressing mode = register 2 -> Sestination regstier =R2 Since the addressing mode and register select fields are all 3 bits long, they correspond to individual octal digits in the octal form of the instruction,. If you wrote it in hex, you'd not be able to pick out the fields so quickly. Disadvantage to octal over hex include ; The numbers are longer (a 16 bit word takes 6 octal digits but only 4 hex digits) Word lengths tend not to be multiples of 3 bits. This means, for example you can't easily split 16 bit word into bytes, or combine 2 bytes into a word when you write them in Octal. In hex it's trivial. There were various split octal notations where you convert each part separately, but they get confusing fast. But basically it's just another way of writing numbers which is useful sometiimes (particularly if 'you're misisng 2 fingers' as Tom Lehrer put it. -tony