Question 4.3.4: Converting from Base 10 to Base 8 Convert 486 to base 8....

We are converting a numeral in base 10 to a numeral in base 8. The positional values in the base 8 system are . . . , 8³, 8², 8, 1, or . . . , 512, 64, 8, 1.

The highest power of 8 that is less than or equal to 486 is 8², or 64. Divide 486 by 64.

­                     First digit in answer
­                    ↓

486 ÷ 64 = 7 with remainder 38

Therefore, there are seven groups of 8² in 486. Next divide the remainder, 38, by 8.

­                Second digit in answer
­                ↓

38 ÷ 8 = 4 with remainder 6

­                                                  ↑
­              Third digit in answer

There are four groups of 8 in 38 and 6 units remaining. Since the remainder, 6, is less than the base, 8, no further division is required.

= (7 × 64) + (4 × 8) + (6 × 1)

= (7 × 8²) + (4 × 8) + (6 × 1)

= 746_8

Notice that we placed the subscript 8 to the right of 746 to show that it is a base 8 numeral.