UGC NET CSE | November 2017 | Part 2 | Question: 2

Question

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 1

(313)=3*16+4*1+3=55;

(322)=3*16+4*2+2=58;

addtition is 55+58=113....

now 113 in base 4 can be represented as ...1301 to the base 4...

ANS is 4)

Answer 2

Add each digit of two numbers from right to left:
3+2 =5 which in base 4 will be 11. So 1 will be in result and 1 will be the ""carry"" to next step
1+2+1(carry from the last step)=4 which in base 4 will be 10. So 0 will be in result and 1 will be the ""carry"" to next step
3+3+1(carry from the last step)=7 which in base 4 will be 13. So 3 will be in result and 1 will be the carry 

Answer is  (1301) ₄

Answer 3

Decimal	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Quaternary	0	1	2	3	10	11	12	13	20	21	22	23	30	31	32	33

     313                                    

+   322

_________

   1301

Answer 4

m=313 its binary equivalent is (110111)₂

n=322 its binary equivalent is   (111010)₂

then add   (110111  +  111010)₂  we get (1110001)₂

so   (1 11 00 01)₄  = (1301)4                  

ans is 4