415 octal to binary

Here we will show you how to convert the octal number 415 to a binary number. First note that the octal number system has eight different digits (0 1 2 3 4 5 6 7) and the binary number system has only two different digits (0 and 1).

The four steps used to convert 415 from octal to binary are explained below.

Step 1)
Multiply the last digit in 415 by 8⁰, multiply the second to last digit in 415 by 8¹, multiply the third to last digit in 415 by 8², multiply the fourth to last digit in 415 by 8³, and so on, until all the digits are used:

5 × 8⁰ = 5
1 × 8¹ = 8
4 × 8² = 256

Step 2)
Next, we add up all the products we got from Step 1, like this:

5 + 8 + 256 = 269

Step 3)
Now we divide the sum from Step 2 by 2. Put the remainder aside. Then divide the whole part by 2 again, and put the remainder aside again. Keep doing this until the whole part is 0.

269 ÷ 2 = 134 with 1 remainder
134 ÷ 2 = 67 with 0 remainder
67 ÷ 2 = 33 with 1 remainder
33 ÷ 2 = 16 with 1 remainder
16 ÷ 2 = 8 with 0 remainder
8 ÷ 2 = 4 with 0 remainder
4 ÷ 2 = 2 with 0 remainder
2 ÷ 2 = 1 with 0 remainder
1 ÷ 2 = 0 with 1 remainder

Step 4)
In the final step, we take the remainders from Step 3 and put them together in reverse order to get our answer to 415 octal to binary:

415 octal = 100001101 binary

Octal to Binary Converter
Here you can convert another octal number to binary. Remember, octal numbers only include digits 0 through 7.

416 octal to binary
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