CAT 2025 Lesson : Number Systems - Conversion to other Bases

To convert a number from base

10

to base b, successively divide the number by b till we get a quotient of

0

.

The remainders from bottom to top are the digits of the number (in base b) from left to right.

The decimal number

523

when written in base

8

∴

(523)_{10} = (1013)_{8}

Answer:

1013

In case you want to verify if your answer is correct, you can convert it back to base

10

(1013)_{8} = (1 \times 8^{3}) + (0 \times 8^{2}) + (1 \times 8^{1}) + (3 \times 8^{0}) = 512 + 8 + 3 = 523

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