Final answer:
To evaluate the expression 313 base 4 - 131 base 4 + 333 base 4, the terms are first converted to base 10, the arithmetic is performed, and then the result can be converted back to base 4, resulting in 1211 base 4.
Step-by-step explanation:
The question involves evaluating an expression with numbers in base 4. Evaluating means we need to perform the arithmetic operations of subtraction and addition on these base 4 numbers: 3134, -1314, and +3334. To solve this, we should first convert each term to its base 10 equivalent, perform the arithmetic in base 10, and then, if needed, convert back to base 4.
Here's the base 10 conversion for each:
- 3134 = 3*(4^2) + 1*(4^1) + 3*(4^0) = 48 + 4 + 3 = 55
- 1314 = 1*(4^2) + 3*(4^1) + 1*(4^0) = 16 + 12 + 1 = 29
- 3334 = 3*(4^2) + 3*(4^1) + 3*(4^0) = 48 + 12 + 3 = 63
Now, performing the arithmetic in base 10 gives:
55 - 29 + 63 = 89
If necessary, we could convert this result back to base 4:
8910 = 12114
Therefore, 3134 - 1314 + 3334 evaluates to 12114 in base 4.