Page 25 - Handout Digital Electronics

1.10 Converting decimal numbers to octal number system

To convert from decimal and octal, two methods will be used; the remainder theorem also called the
division method and integers and the multiplication method for decimal fraction.

Method 1: Using the remainder theorem

Steps

1. Divide the decimal number by 8 and note down the remainder
2. Divide what's left (quotient) by 8 and note the remainder
3. Repeat step 2 until the number is no longer divisible by 8
4. Write down the remainder’s values in reverse order.

Example 1

Convert 17610 in octal to decimal
176
= 22 remainder 0 LSB
8
22 = 2 remainder 6
8
2
= 0 remainder 2 MSB
8

Thus, the Octal equivalent of 17610 is 2608

Method 2: Using the multiplication method to convert decimal fractions to octal system

Steps

1. Write down the decimal fraction
2. Multiply the decimal fraction by 8
3. Write down the whole number part
4. Repeat steps 2 and 3 until the degree of accuracy has been achieved.
5. Write down the whole numbers in the order you produced them.

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