To subtract $211_4$ from $1230_4$, follow these steps:

Step 1: Convert from Base 4 to Decimal

Convert each number to base 10.

Convert $1230_4$ to Decimal:

$1 \times 4^3 + 2 \times 4^2 + 3 \times 4^1 + 0 \times 4^0$ $= 1 \times 64 + 2 \times 16 + 3 \times 4 + 0 \times 1$ $= 64 + 32 + 12 + 0 = 108_{10}$

Convert $211_4$ to Decimal:

$2 \times 4^2 + 1 \times 4^1 + 1 \times 4^0$ $= 2 \times 16 + 1 \times 4 + 1 \times 1$ $= 32 + 4 + 1 = 37_{10}$

Step 2: Perform Subtraction in Decimal

$108 - 37 = 71_{10}$

Step 3: Convert Result Back to Base 4

Divide 71 by 4 and record remainders:

$71 \div 4 = 17 \text{ remainder } 3$ $17 \div 4 = 4 \text{ remainder } 1$ $4 \div 4 = 1 \text{ remainder } 0$ $1 \div 4 = 0 \text{ remainder } 1$

Reading the remainders from bottom to top, $71_{10} = 1013_4$.

Final Answer:

$\mathbf{1013_4}$

Would you like a detailed breakdown of any step?

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Related Questions:

1. Convert $321_4$ to base 10.
2. Add $132_4$ and $210_4$ in base 4.
3. Convert $71_{10}$ to base 5.
4. Subtract $1023_4$ from $3201_4$.
5. Explain why base 4 uses only digits 0-3.

Tip: When converting to base 4, keep dividing by 4 and record remainders!