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

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