Question

Convert 15632 base 7 to base 8​

Answer 1

10521₈

Explanation:

First convert the number from base-7 (septenary) to base-10 (decimal):

`\begin{aligned}15632_7 & = (1 * 7^4)+(5 * 7^3)+(6 * 7^2)+(3 * 7^1)+(2* 7^0)\\& = 2401+1715+294+21+2\\& = 4433_(10)\end{aligned}`

Now convert it from base-10 (decimal) to base-8 (octal).

Divide 4433 by 8 repeatedly until you arrive at a quotient less than 8.

`\implies \rm 4433 / 8 = 554\; r\; 1`

`\implies \rm 554 / 8 = 69\; r\; 2`

`\implies \rm 69 / 8 = 8\; r\; 5`

`\implies \rm 8/ 8 = 1\; r \;0`

Arrange the final quotient and the remainders of all the divisions in the bottom-to-top direction:

• 10521₈