Question

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

Answer 1

$\textbf{\underline{Answer :}}$

Given that,

m = (313)₄

n = (322)₄

Now,

m = (313)₄

= [ (3 × 4²) + (1 × 4¹) + (3 × 4⁰) ]₁₀

= [ (3 × 16) + (1 × 4) + (3 × 1) ]₁₀

= (48 + 4 + 3)₁₀

= (55)₁₀

and

n = (322)₄

= [ (3 × 4²) + (2 × 4¹) + (2 × 4⁰) ]₁₀

= [ (3 × 16) + (2 × 4) + (2 × 1) ]₁₀

= (48 + 8 + 2)₁₀

= (54)₁₀

Now, m + n

= (313)₄ + (322)₄

= (55)₁₀ + (54)₁₀

= (99)₁₀

Now,

4 | 99
--------
4 | 24 ------> remainder = 3
--------
4 | 6 --------> remainder = 0
-------
4 | 1 ---------> remainder = 2

So, (99)₁₀ = (1203)₄

Hence, m + n

= (313)₄ + (322)₄

= (1203)₄

#$\textbf{MarkAsBrainliest}$

Answer 2

Answer:

first convert  (313) into base of 4 = 3*4(2) its 4 ka square + 1*4(1) + 3*4(0)=55

now for second (322) into base of 4 = 3*4(2) its 4 ka square + 2*4(1) + 2*4(0)=58

now we will add 55+58=113

now again convert (113) base of 4 = Answer

1*4(2)+1*4(1)+3*4(0)=1301

calculation if u do mistake for referencer

1) 3*4(2) =48

2) 1*4(1) =4

3) 3*4(0) =3

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total     55

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