UGC NET COMPUTER SCIENCE AND APPLICATIONS PAPER - 2 Question 2 November 2017 Solution

Q: 2 Let m=(313)₄ and n=(322)₄ . Find the base 4 expansion of m+n.

(1) (635)₄

(2) (32312)₄

(3) (21323)₄

(4) (1301)₄

Answer: (4)

Explanation:

Firstly convert m & n into base 10:

(313)₄ = 3*4²+1*4¹+3*4⁰ = (55)₁₀
(322)₄ = 3*4²+2*4¹+2*4⁰  = (58)₁₀

Now m + n = 55+58 = (113)₁₀

Now Convert (113)₁₀ into base 4

• When 113 is divided by 4, the quotient is 28 and the remainder is 1.
• When 28 is divided by 4, the quotient is 7 and the remainder is 0.
• When 7 is divided by 4, the quotient is 1 and the remainder is 3.
• When 1 is divided by 4, the quotient is 0 and the remainder is 1.

Write the remainders from bottom to top.

So, (113)₁₀ = (1301)₄      which is Correct.