Question

How do you convert decimals to octal and vice versa?

Answer 1

Are you looking for a step-by-step explanation for both converting decimals to octal and octal to decimal, or do you want a brief overview of each process?

Answer 2

Converting between decimal and octal (base-8) involves a few steps for each direction:

### Decimal to Octal

1. **Divide the Decimal Number**: Divide the decimal number by 8 and keep track of the quotient and remainder.
2. **Repeat**: Continue dividing the quotient by 8 until the quotient is 0, each time noting the remainder.
3. **Read the Remainders**: The octal number is the sequence of remainders read from bottom to top.

**Example**: Convert 156 (decimal) to octal.

- 156 divided by 8 is 19 with a remainder of 4.
- 19 divided by 8 is 2 with a remainder of 3.
- 2 divided by 8 is 0 with a remainder of 2.

Reading the remainders from bottom to top gives 234 in octal.

### Octal to Decimal

1. **Multiply Each Digit**: Multiply each digit of the octal number by 8 raised to the power of its position, starting from 0 on the right.
2. **Sum the Values**: Add all these values together to get the decimal number.

**Example**: Convert 234 (octal) to decimal.

- 2 × 8^2 = 2 × 64 = 128
- 3 × 8^1 = 3 × 8 = 24
- 4 × 8^0 = 4 × 1 = 4

Adding these values gives 128 + 24 + 4 = 156 in decimal.