Converting decimal numbers to a given base

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Tarheel123

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I have two problems here that I have no clue how to do. Could someone show me step by step?

Convert the decimal number to given base

1 503 to base 8
2 13,562 to base 8
 
Tarheel123 said:
I have two problems here that I have no clue how to do. Could someone show me step by step?

Convert the decimal number to given base

1 503 to base 8
2 13,562 to base 8
Click to expand...
There is a procedure (based on the Euclidean Algorithm) which works well.

1) Divide 503 by 8. .Note the remainder.
. . . 503 ÷ 8 .= .62 . . . rem. 7

2) Divide the <u>quotient</u> by 8. .Note the remainder.
. . . 62 ÷ 8 .= .7 . . . . . rem. 6

Repeat step (2) until it "comes out even".

Divide 7 by 8. .Note the remainder.
. . . 7 ÷ 8 .= .0 . . . . . . rem. 7

Now read up (↑) the remainders.

Answer: . 503 . = . 767<sub>8</sub>

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Check

767<sub>8</sub> . = . 7(8<sup>2</sup>) + 6(8) + 7(1) . = . 448 + 48 + 7 . = . 503 . . . yay!

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

I'll let you try it on the second problem.
. . . You should get: 323728<sub>8</sub>
.
 
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