the sum of two unsigned 12-bit octal numbers

Question

I'm trying to understand why my calculation is giving different answer than the book.

The question ask what is the sum of A & B if they represent unsigned 12-bit octal numbers?

A=3174 and B=0522

Below is my approach to the problem:

1. 3174 octal = 011001111100 (unsigned 12 bits)
   0522 octal = 000101010010 (unsigned 12 bits) 
          sum = 011111001110 (unsigned 12 bits)

Second approach I added the two octal number straight no need converting to binary

3174 octal+0522 octal= 3716 octal (answer must be in octal). 

But I don't get it how the book ended getting 7620 confused // this is in MIPS programming

Answer 1

This is exercise 3.1.1 of Computer Organization and Design, Revised 4^th Edition.

Your math is correct. Check it with Wolfram Alpha.

3174₈ + 0522₈ = 3716₈

The solutions guide for the book says the answer is 7620. (That's what I can make out through the blur over page 68 on scribd.)

Of the four numbers in the table for that exercise, there is no pair that sums to 7620₈ or 7620₁₀, whether you interpret the numbers in the table as octal or decimal. The solutions guide is either wrong, or using a very obscure interpretation of the question.

Here's the Mathematica code I used to verify:

inputs = {3174, 0522, 4165, 1654, 8^^3174, 8^^0522, 8^^4165, 8^^1654}
Table[{i + j, BaseForm[i + j, 8]}, {i, inputs}, {j, inputs}] // Flatten // Sort // TableForm