finite table

Question

Using the completed table, compute 747₈×56₈

   1 2 3 4 5 6 7
1 1 2 3 4 5 6 7
2 2 4 6 10 12 14 16
3 3 6 11 14 17 22 25
4 4 10 14 20 24 30 34
5 5 12 17 24 31 36 43
6 6 14 22 30 36 44 52
7 7 16 25 34 43 52 61

Answer 1

How nice to see a problem using Octal.

This table makes the math as simple as using the multiplication table in decimal.  Just remember that the number system has only 0-7.

          1     2     3     4     5      6      7

   -----------------------------------------
1 |     1     2     3     4     5      6     7
2 |     2     4     6   10   12    14    16
3 |     3     6   11   14   17    22    25
4 |     4   10   14   20   24    30    34
5 |     5   12   17   24   31    36    43
6 |     6   14   22   30   36    44    52
7 |     7   16   25   34   43    52    61
 
So, for example, 6*5 is 36.  That means, when multiplying, to put down 6 and carry the 3.  This table is for multiplication – we assume that you can add in Octal.  If not, use eight of your fingers (handy, because you just don’t use thumbs).

O.K. the problem:   7478×568

Like primary school math:     747

                                              x  56
                                            --------

6*7 is 52 (read as “five-two,” not as “fifty-two”).  Put down the 2 and carry the 5.
6*4 is 30, plus 5 is 35, so put down 5 and carry 3.
6*7 id 53, plus 3 is 55.  On this line 5552.

5*7 is 43.  Put down 3 and carry 4.
5*4 is 24, plus 4 is 30.  Put down 0 and carry 3.
5*7 is 43, plus 2 is 45.
On this line, 4503.

Add in octal    5552
                        4503
                    ---------
                      53602

Now, converting to and from decimal (because we usually think in decimal) helps in this process – if you can remember what the number means (that’s why we say “five-two,” for example).  So, with 6*7, we could calculate that in decimal and get 42, then convert that to 52 octal (that is, 5*8+2).  This process gets easier with practice.