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

Add the two numbers directly in base 4 using carries.

• Units place: 3 + 2 = 5, which is 1 with a carry of 1 because 5 = 4 + 1.

• Fours place: 1 + 2 + carry 1 = 4, which is 0 with a carry of 1.

• Sixteens place: 3 + 3 + carry 1 = 7, which is 3 with a carry of 1.

• Final carry becomes the 4^3 place: 1.

Therefore, m + n = (1301)₄.

Check (optional): Convert to decimal: (313)₄ = 3·16 + 1·4 + 3 = 55; (322)₄ = 3·16 + 2·4 + 2 = 58; sum = 113. Convert 113 to base 4: 113 ÷ 64 = 1 remainder 49; 49 ÷ 16 = 3 remainder 1; 1 ÷ 4 = 0 remainder 1; remainder 1 → (1301)₄.