Converting Octal Number 47227 to Binary

How do we convert the octal number 47227 to binary?

To convert octal number 47227 to binary, what are the necessary steps we need to take?

Steps to Convert Octal Number 47227 to Binary:

To convert the octal number 47227 to binary, follow these steps:

Firstly, we need to convert the octal number 47227 to decimal, and then from decimal to binary.

The binary representation of octal number 47227 is 101101111001101.

To convert from octal to decimal, we use the positional notation system, where each digit represents a power of 8. So, we have:

4*8^4 + 7*8^3 + 2*8^2 + 2*8^1 + 7*8^0 = 20,023

Now, to convert from decimal to binary, we use the binary division method, where we divide the decimal number by 2 and keep track of the remainders. We continue dividing until we reach 0.

20,023 / 2 = 10,011 remainder 0

10,011 / 2 = 5,005 remainder 1

5,005 / 2 = 2,502 remainder 1

2,502 / 2 = 1,251 remainder 0

1,251 / 2 = 625 remainder 1

625 / 2 = 312 remainder 1

312 / 2 = 156 remainder 0

156 / 2 = 78 remainder 0

78 / 2 = 39 remainder 0

39 / 2 = 19 remainder 1

19 / 2 = 9 remainder 1

9 / 2 = 4 remainder 1

4 / 2 = 2 remainder 0

2 / 2 = 1 remainder 0

1 / 2 = 0 remainder 1

Therefore, the binary representation of octal number 47227 is 101101111001101.