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The places in base two (binary) are ones, twos, fours, eights, sixteens, thirty-twos and so on.

There is one 32 in 47 with 15 left over. There is one 8 in 15 with 7 left over. There is one 4 in 7 with 3 left over. There is one 2 in 3 with 1 left over. There is one 1 in 1 with 0 left over.

That leaves us with one 32, one 8, one 4, one 2 and one 1.

47 base 10 = 10 1111 base 2

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8y ago
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9y ago

Partition the sum 47 into powers of 2.

Put these powers of 2 in descending order.

Replace the powers of 2 by 1 while inserting 0 for powers that do not appera.


Thus,

47 = 32 + 8 + 4 + 2 + 1 or 2^5 + 2^3 + 2^2 + 2^1 + 2^0 (note that 2^4 is missing).


And so the binary form is 101111.


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Q: What are the steps to convert decimal number 47 to binary number?
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