Number representation and calculations

Question

Add

574₈

605₈

           

 

Answer 1

Moving right to left:

 

4 + 5         is    1 carry 1      [that is 11₈ or 9₁₀]

1 + 7 + 0   is    0 carry 1

1 + 5 + 6   is    4 carry 1

1  carried  is     1

 

The result is 1401₈.

 

Note: If you use your fingers to count (like preschool), 4 + 5 is four, five, six, seven, one-zero, one-one.  So, put down one and carry one.

Answer 2

The octadecimal system has only digits 0, 1, 2, 3, 4, 5, 6, 7.

 

We will construct our answer one digit at a time.

 

We will organize our answer horizontally.

 

4 + 5 = 9.

 

But 9>=8.

 

Then, 

4₈+5₈ = 1x8 +1 = 11₈                                                                                          _  _ _ 1

 

The last digit of the answer is 1, and we have to add 1 to the next set of digits.

 

7₈+0₈+1₈ = 10₈                                                                                                     _ _ 0 1

 

The second last digit is 0 and we have to add 1 to the next position digits addition.

 

We add the third position digits and 1 we have left over from second position.

 

5₈+6₈+1₈=14₈                                                                                                               1 4 0 1₈

 

The final number will have 4 digits: 1401₈.