Page 26 - Handout Digital Electronics

Example 1:

Convert 0.062510 to octal number system equivalent

.0625  8 = 0.500 whole number part = 0 MSB
.500  8 = 4. 000 whole number part = 4 LSB

Thus, the Octal equivalent of 0.062510 is 0.48

Example 2:

Convert 176.062510 to octal equivalent

This example involves converting mixed decimal numbers to octal. Use the steps below to convert such
numbers:

Steps

1. Use the remainder theorem to convert the decimal number to octal
2. Use the multiplication method to convert the decimal fraction to octal fraction
3. Write the octal integer part, followed by a period and then the fraction part.

We convert the whole number (integer) part using the division method

176
= 22 remainder 0 LSB
8
22 = 2 remainder 6
8
2
= 0 remainder 2 MSB
8

Thus, the octal equivalent is 2608

We convert the fraction part (0.062510) to binary equivalent using the multiplication method.

.0625  8 = 0.500 whole number part = 0 MSB
.500  8 = 4. 000 whole number part = 4 LSB

Therefore 176.062510 is equivalent to 260.048

1.11 Converting decimal numbers into Hexadecimal number system

The steps used to convert decimal numbers too binary and to octal also apply when converting decimal
numbers to hexadecimal.

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