Question

The octal equivalent of (177)₁₀ is:
1. (231)₈
2. (251)₈
3. (261)₈
4. (162)₈

Answer 1

Correct Answer - Option 3 : (261)₈

CONCEPT:

• Following are the steps to convert decimal to octal:

1. If the provided decimal number is less than the number 8 then the octal number is the same.
2. If the provided decimal number is larger than 7 then divide it by number 8.
3. take a note of the remainder, received after division
4. Repeat step 2 and 3 with the quotient until it is less than 8
5. Now, note the remainders in the reverse order (bottom to top)
6. The resultant thus received is the equivalent octal number to the provided decimal number.
    

Explanation:

Decimal Number	Operation	Quotient	Remainder	Octal Number
177	÷ 8	22	1	1
22	÷ 8	2	6	61
2	÷ 8	0	2	261

 

Hence, (177)10 = (261)8