Convert Decimal Numbers to Octal Using the Sum-of-Weights Method

How can we convert decimal numbers to octal using the sum-of-weights method?

What is the process involved in converting decimal numbers to octal using the sum-of-weights method?

Answer:

To convert decimal numbers to octal using the sum-of-weights method, you need to divide the decimal number by 8 repeatedly until the quotient is 0. Write down the remainders in reverse order to get the octal equivalent.

The process of converting decimal numbers to octal using the sum-of-weights method involves dividing the decimal number by 8 repeatedly until the quotient is 0. Write down the remainders in reverse order to obtain the octal equivalent.

For example:

a) For 967:
967 ÷ 8 = 120 remainder 7
120 ÷ 8 = 15 remainder 0
15 ÷ 8 = 1 remainder 7
1 ÷ 8 = 0 remainder 1
So, 967 in decimal is 1767 in octal.

b) For 345:
345 ÷ 8 = 43 remainder 1
43 ÷ 8 = 5 remainder 3
5 ÷ 8 = 0 remainder 5
So, 345 in decimal is 513 in octal.

c) For 617:
617 ÷ 8 = 77 remainder 1
77 ÷ 8 = 9 remainder 5
9 ÷ 8 = 1 remainder 1
1 ÷ 8 = 0 remainder 1
So, 617 in decimal is 1151 in octal.

This method allows you to convert decimal numbers to octal efficiently and accurately. By following the steps outlined above, you can easily determine the octal equivalent of any decimal number.