342-173 solve this equation in base 8 (the answer in base 10 is 169)

Question

solve in base 8 or octal

Answer 1

342

-173

_____

You can't take 3 from 2 (2 is less than 3) so you look at the 4 in the eights place.

Now that's really 4 eights, so you make it 3 eights, regroup, then you change the 8 to 8 ones, then you add 'em to the 2. You get 1 2 base 8 which is 10(10) and you take away 3.

That's 7. Okay?

Now, instead of 4 in the eights place, you've got 3, because you added 1 (that is to say, 8) to the 2.

But you can't take 7 from 3 so you look at the sixty-fours.

Sixty-four.... how did sixty-four get into it, I hear you cry? Well 64 is eight squared, don't you see. Ask a silly question, you get a silly answer.

From the 3, you then use 1 to make 8 ones. You add those ones to the 3 and you get 13(8) or in other words in base 10 you have 11 and you take away 7 - and 7 from 11, that's 4!

Now go back to the sixty-fours, you're left with 2 and you take away 1 from 2, and that leaves...

Everybody get 1?

New Math. It's so simple, that only a child can do it.

Answer 2

342 - 173 = 147 in base 8. The base 10 equivalent is 226 - 123 = 103.

Answer 3

Convert given base-10 numbers, (342)10 and (173)10, to base-8 using remainder method.

342÷8=42 R6, 42÷8=5 R2, 5÷8=0 R5, so (342)10=(526)8

173÷8=21 R5, 21÷8=2 R5, 2÷8=0 R2, so (173)10=(255)8

Thus, (342)10-173(10)=(526)8-(255)8

* Expand (526)8, (255)8 with power of 8, using the fact that each place in a base-8 number represents a power of 8.

(526)8=5x8²+2x8¹+6x8º=(5-1)x8²+(8+2)x8¹+6x8º, and (255)8=2x8²+5x8¹+5x8º   

We have: (526)8-(255)8=(5-1-2)x8²+(8+2-5)x8¹+(6-5)x8º=2x8²+5x8¹+1x8º

** That is: (526)8-(255)8=(251)8

CK: (251)8=2x8²+5x8¹+1x8º=128+40+1=(169)10=(342)10-(173)10   CKD.

The answer is: (342)10-(173)10=(526)8-(255)8=(251)8

* If you familia with borrowing in base-8 subtraction, just skip this part and go to **.