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CAT 2025 Lesson : Number Systems - Conversion to other Bases

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4. Conversion from Decimal to a different base

To convert a number from base
1010 to base b, successively divide the number by b till we get a quotient of 00.

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

Example 4

The decimal number 523523 when written in base 88 is

Solution



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

Answer:
10131013


In case you want to verify if your answer is correct, you can convert it back to base
1010.
(1013)8=(1×83)+(0×82)+(1×81)+(3×80)=512+8+3=523(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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