UGC-NET | UGC-NET CS 2017 Dec 2 | Question 2

Let m=(313)4 and n=(322)4. Find the base 4 expansion of m+n.
(A) (635)4
(B) (32312)4
(C) (21323)4
(D) (1301)4


Answer: (D)

Explanation: We have m=(313)4 and n=(322)4 convert m and n into decimal:

m = 3*42 + 1*41 + 3*40
m = 48 + 4 + 3
m = 55.
Now n=3*42 + 2*41 +2*40
    n = 48 + 8 +2
    n = 58.
m + n = 55 + 58 
m + n = 113

Now we have to convert 113 in to base 4:

ie step 1-113 % 4 = 1
          113 / 4 = 28
   step 2- 28 % 4 = 0
           28 / 4 = 7
   step 3- 7 % 4  = 3
           7 / 4  = 1
   step 4- 1 % 4  = 1
           1 / 4  --> will not divide it in quant. 
So we have to stop here.

The answer will be Residue from step 4 to step 1 inorder ie 1301
Ans-(1301)4

Quiz of this Question

My Personal Notes arrow_drop_up
Article Tags :

2


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.