Octal

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