numbering system 2

Question

1142 – 921 = 821, then 1674 – 788 = ?

Answer is EEC by hexadecimal subtraction

Comments

It is in hexadecimal only.

$1674-788$

Now, for last two digit ,as 4 less than 8, add 16 with 4, i.e. $20-8=12$. $ i.e.C$

Similar forother digits too

Answer 1

$1142 – 921 = 821 $

For solving it fast logically, first find the preconditions. We can see that one number is 921, means the base must be greater than 9. As the base is greater than 9, subtracting last two digits 42-21 gives us 21 which is obvious. when we see 1-8, we take "borrow" from left hand side. And hence 11-9 is performed, but the result is 8 ! In decimal 17-9 gives us 8. Hence $11_x$ must be $17_{10}$

And we know that 11 in Hexadecimal gives 17 in decimal. Hence we conclude that base is 16.

Now perform quick subtraction :

	1	6	7	4
-		7	8	8
	0	Take Borrow (5+16)-7=14=E	Take borrow (6+16)-8=14=E	Take borrow (4+16)-8=12=C

Hence the ans is $EEC$