157 octal to binary

Here we will show you how to convert the octal number 157 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 157 from octal to binary are explained below.

Step 1)
Multiply the last digit in 157 by 8⁰, multiply the second to last digit in 157 by 8¹, multiply the third to last digit in 157 by 8², multiply the fourth to last digit in 157 by 8³, and so on, until all the digits are used:

7 × 8⁰ = 7
5 × 8¹ = 40
1 × 8² = 64

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

7 + 40 + 64 = 111

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.

111 ÷ 2 = 55 with 1 remainder
55 ÷ 2 = 27 with 1 remainder
27 ÷ 2 = 13 with 1 remainder
13 ÷ 2 = 6 with 1 remainder
6 ÷ 2 = 3 with 0 remainder
3 ÷ 2 = 1 with 1 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 157 octal to binary:

157 octal = 1101111 binary

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

160 octal to binary
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