Question

Using the Division algorithm to find q and r such that 3662 = q·16+r , where 0 ≤ r < 16 . What if we take c = −3662 instead of c = 3662 ? From this example we learn that q is the largest integer less than or equal to c/b .

Answer 1

Answer:

a) If c=3662 then q=228 and r=14.

b) If c=-3662, then q=-229 and r=2

Step-by-step explanation:

a) Observe that 229*16=3664, since r must be in the interval [0,16), then 229 doesn't work, but 228*16=3648 and 3662-3648=14.

Then 3662=228*16+14.

b) Observe that -228*16=-3648 and -3648-14=-3662, but r= must be positive. Then -228 doesn't work.

But observe that -229*16=-3664 and -3664+2=-3662. So -3662=-229*16+2