Subtract 211 base 4 from 1230 base 4 (2 marks)

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!

Learn how to subtract 211 base 4 from 1230 base 4 with a detailed step-by-step solution. This problem covers number system conversions, base 4 subtraction, and base 10 conversion techniques. Suitable for students in Grades 7-10.

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