Is there anyone smarter in DLD????

Question

Add,subtract and multiply the following octal and hexadecimal numbers without converting to decimal?

(371)8 and (256)8

(2EC)16 and (7B)16 (where 8 & 16 are in the subscript)

Answer 1

371

256

____

add

6 + 1 =7

7 + 5 = 14, put in 4, carry 1

1 + 3 + 2 = 6

ans = 647

371

256

____

subtract

1-6, borrow 1. 11-6 = 3

borrow reduces 7 to 6. 6-5=1

3-2 =1

answer 113

2EC

07B

add

B+C = 23(10) = 17(16), keep 7 and carry 1

1+7+E = 14+1+7 = 22(10) = 16(16), keep 6 and carry 1

1+2 = 3

answer 367

.

Answer 2

647

367

You can make an addition table for any system with a natural number base much like the base 10 table you grew up with.  This page has both octal and hexadecimal tables (as well as binary and decimal):

http://www.marlenesite.com/math/basearit...

Although, the tables should really all start with 0.  That's why there are only 15 entries in that hexadecimal table (it's missing 0).