leo donahue

Ranch Hand

Posts: 327

posted 14 years ago

I've searched the web, this forum and still can't find a simple explanation of converting Decimal to Octal. Most of the www links on Google that look promising, don't work.

As I understand it, all Octal numbers are prefixed with a '0'. What really gripes me is that most of the web resources just say to "add one" when you get past the decimal number '7'. Add one to where?

Can't I just divide the decimal number by 8 and then add the remainder at the far right?

i.e.:

1 = 01

2 = 02

...

7 = 07

8 = ((8/8) + remainder of '0') = 010

16= 020

24= 030

31= 037

100 = 0124

Is this right to assume this?

[ May 15, 2003: Message edited by: leo donahue ]

As I understand it, all Octal numbers are prefixed with a '0'. What really gripes me is that most of the web resources just say to "add one" when you get past the decimal number '7'. Add one to where?

Can't I just divide the decimal number by 8 and then add the remainder at the far right?

i.e.:

1 = 01

2 = 02

...

7 = 07

8 = ((8/8) + remainder of '0') = 010

16= 020

24= 030

31= 037

100 = 0124

Is this right to assume this?

[ May 15, 2003: Message edited by: leo donahue ]

Thanks, leo

Jim Yingst

Wanderer

Sheriff

Sheriff

Posts: 18671

posted 14 years ago

You've almost got it.

100 is not 0124 as you would get with your method (which works for numbers up to 64), it's 0144

The general rule of thumb for converting from decimal to base x is as follows:

Divide the decimal by the highest power of x that is less than a decimal. Write down the integer part of the result, lop it off, and use the remainder with the next-lowest power of x. Stop when you get power of x = 0.

Sound confusing? Yes, so here's an example:

Convert 100 to base 8.

8^2 = 64; 8^3 = 512. We start with 64, since it is less than 100.

100 / 64 = 1.5625 ( 1 r 36). Write down the 1 and use the remainder to repeat for the next lower power of 8 (which is 8^1, or 8)

36 / 8 = 4.5 ( 4 r 4) Write down the 4 (now our number is 14) and use the remainder to repeat for the next lower power of 8. The next lower power is 8^0, or 1.

4 / 1 = 4 (we could have just written down the remainder without carrying out this step, of course.... ) so now we just write down the 4 coming up with the result 144.

Try this for 71.

71 / 64 = 1.109375 (1 r7)

7 / 8 = 0.875 (0 r7)

7 / 1 = 7.0

Result? 107; therefore, 71 in base 10 is 107 in base 8.

You can now use this to prove that Christmas == Halloween. (DEC 25 = OCT 31)

[ May 15, 2003: Message edited by: Joel McNary ]

100 is not 0124 as you would get with your method (which works for numbers up to 64), it's 0144

The general rule of thumb for converting from decimal to base x is as follows:

Divide the decimal by the highest power of x that is less than a decimal. Write down the integer part of the result, lop it off, and use the remainder with the next-lowest power of x. Stop when you get power of x = 0.

Sound confusing? Yes, so here's an example:

Convert 100 to base 8.

8^2 = 64; 8^3 = 512. We start with 64, since it is less than 100.

100 / 64 = 1.5625 ( 1 r 36). Write down the 1 and use the remainder to repeat for the next lower power of 8 (which is 8^1, or 8)

36 / 8 = 4.5 ( 4 r 4) Write down the 4 (now our number is 14) and use the remainder to repeat for the next lower power of 8. The next lower power is 8^0, or 1.

4 / 1 = 4 (we could have just written down the remainder without carrying out this step, of course.... ) so now we just write down the 4 coming up with the result 144.

Try this for 71.

71 / 64 = 1.109375 (1 r7)

7 / 8 = 0.875 (0 r7)

7 / 1 = 7.0

Result? 107; therefore, 71 in base 10 is 107 in base 8.

You can now use this to prove that Christmas == Halloween. (DEC 25 = OCT 31)

[ May 15, 2003: Message edited by: Joel McNary ]

Piscis Babelis est parvus, flavus, et hiridicus, et est probabiliter insolitissima raritas in toto mundo.

posted 14 years ago
Piscis Babelis est parvus, flavus, et hiridicus, et est probabiliter insolitissima raritas in toto mundo.

BTW, To reconstruct the decimal you work backwards. 124 base 8 is

1 * (8^3) + 2 * (8^1) + 4 * (8^0)

1 * 64 + 2 * 8 + 4 * 1

64 + 16 + 4

84

[RANDOM DIGRESSION]

84, BTW, is the name of the town in which I grew up. Except the Post Office spelled it out, "Eighty Four"

[/RANDOM DIGRESSION]

1 * (8^3) + 2 * (8^1) + 4 * (8^0)

1 * 64 + 2 * 8 + 4 * 1

64 + 16 + 4

84

[RANDOM DIGRESSION]

84, BTW, is the name of the town in which I grew up. Except the Post Office spelled it out, "Eighty Four"

[/RANDOM DIGRESSION]