Decimal (base-10) to octal (base-8) conversion:

Step 1: Divide the decimal number by 8 (8 comes from the base value of octal number system).

Step 2: The remainder is the LSD (least significant digit) of the octal number.

Step 3: Divide the quotient from*Step 1* by 8 again.

Step 4: The new remainder from*Step 3* is the next digit (from right to left) of the octal number.

Step 5: The process continues until we get 0 as the quotient. The remainder from this step is the MSD (most significant digit) of the octal number.

Step 2: The remainder is the LSD (least significant digit) of the octal number.

Step 3: Divide the quotient from

Step 4: The new remainder from

Step 5: The process continues until we get 0 as the quotient. The remainder from this step is the MSD (most significant digit) of the octal number.

Decimal number: 45_{10}

Numerator | Denominator | Quotient | Remainder |
---|---|---|---|

45 | 8 | 5 | 5 (LSD) |

5 | 8 | 0 | 5 (MSD) |

So, the octal representation: 55_{8}

Decimal fraction to octal (base-8) conversion:

Step 1: Multiply the fraction number by 8 (8 comes from the base value of octal number system).

Step 2: The result (without the fraction part if any) is the MSD of the octal number.

Step 3: Take only the fraction part from*Step 2* and multiply it by 8 again.

Step 4: The result (except the fraction part if any) from*Step 3* is the next digit (from left to right) of the octal number.

Step 5: The process continues until we get X.00 as the final result (here X = any number from 0 to 7). From this step X is the LSD of the octal number.

Step 2: The result (without the fraction part if any) is the MSD of the octal number.

Step 3: Take only the fraction part from

Step 4: The result (except the fraction part if any) from

Step 5: The process continues until we get X.00 as the final result (here X = any number from 0 to 7). From this step X is the LSD of the octal number.

Decimal number: 0.8125_{10}

Steps | Multiplicand | Multiplier | Result (without fraction part) | Result (only the fraction part) |
---|---|---|---|---|

1 | .8125 | 8 | 6 (MSB) | .5 |

2 | .5 | 8 | 4 (LSB) | .0 |

So, the octal representation: .64_{8}

Decimal: 45.8125_{10}

Octal: 55.64_{8}

Octal (base-8) to decimal (base-10) conversion:

From right (LSB) to left (MSB) we will take each digit and multiply them by 8^{x} and later add the results together. Here x is the corresponding position of a digit and 8 comes from the base value of octal number system.

Octal number: 55_{8}

Number: | 5 (MSB) | 5 (LSB) |
---|---|---|

Position: | 1 | 0 |

(5 x 8^{1}) + (5 x 8^{0})

= 40 + 5

= 45

So, the decimal representation: 45_{10}

= 40 + 5

= 45

So, the decimal representation: 45

Octal fraction to decimal fraction conversion:

From left (MSB) to right (LSB) we will take each digit and multiply them by 8^{x} and later add the results together. Here x is the corresponding position of a digit and 8 comes from the base value of octal number system.

Octal number: .64_{8}

Number: | 6 (MSB) | 4 (LSB) |
---|---|---|

Position: | -1 | -2 |

(6 x 8^{-1}) + (4 x 8^{-2})

= 0.75 + 0.0625

= 0.8125

So, the decimal representation: 0.8125_{10}

= 0.75 + 0.0625

= 0.8125

So, the decimal representation: 0.8125

Octal: 55.64_{8}

Decimal: 45.8125_{10}