Octal Help (octal to decimal)


Here is one way to convert a octal number to a decimal number.

First you need to know your binary numbers up to 7.

Decimal    Binary
=================
    0          0
    1          1
    2         10
    3         11
    4        100
    5        101
    6        110
    7        111

Make each binary number 3 digits.

Decimal    Binary
=================
    0        000
    1        001
    2        010
    3        011
    4        100
    5        101
    6        110
    7        111

We are going to go from octal to binary to decimal.

For example:

437 (octal)

Take each digit and convert to binary.

4 = 100
3 = 011
7 = 111

Then put all the binary numbers together starting with the first or most significant digit.

100011111

Take the binary number and convert to decimal.

256 128 64 32 16 8 4 2 1
  1   0  0  0  1 1 1 1 1

100011111 = 287 (decimal)

437 (octal) = 287 (decimal)


Another example:

1065 (octal)

Take each digit and convert to binary.

1 = 001
0 = 000
6 = 110
5 = 101

Then put all the binary numbers together starting with the first or most significant digit.

001000110101

Leading zeros (zeros on the left before the first one) in binary have no value so we can delete the first two zeros.

1000110101

So 001000110101 and 1000110101 is the same value when converted to decimal.

512 256 128 64 32 16 8 4 2 1
  1   0   0  0  1  1 0 1 0 1

1000110101 = 565 (decimal)

1065 (octal) = 565 (decimal)