Decimal to Binary Conversion Examples for AP CSP

📚 Quick Study Guide: Decimal to Binary Conversion

• 💡 The most common method for converting a decimal (base-10) number to a binary (base-2) number is the "division by 2" method.
• ➗ To start, repeatedly divide the decimal number by 2.
• 📝 At each division step, record the remainder. This remainder will always be either 0 or 1.
• 🛑 Continue this process until the quotient (the result of the division) becomes 0.
• ⬆️ The binary number is formed by reading the remainders from bottom to top (the last remainder you recorded becomes the most significant bit, and the first remainder becomes the least significant bit).
• ✨ Example: Convert $13_{10}$ to binary
  • $13 \div 2 = 6$ remainder $1$
  • $6 \div 2 = 3$ remainder $0$
  • $3 \div 2 = 1$ remainder $1$
  • $1 \div 2 = 0$ remainder $1$
  • Reading the remainders from bottom to top gives us $1101_2$.

🧠 Practice Quiz: Decimal to Binary

1. Convert decimal $25_{10}$ to its binary equivalent.

• A) $11001_2$
• B) $10110_2$
• C) $11010_2$
• D) $10001_2$

2. What is the binary representation of decimal $42_{10}$?

• A) $101010_2$
• B) $101100_2$
• C) $101001_2$
• D) $110100_2$

3. Convert decimal $7_{10}$ to binary.

• A) $101_2$
• B) $110_2$
• C) $011_2$
• D) $111_2$

4. Which binary number is equivalent to decimal $100_{10}$?

• A) $1100100_2$
• B) $1101000_2$
• C) $1110100_2$
• D) $1100010_2$

5. What is $50_{10}$ in binary?

• A) $110010_2$
• B) $110100_2$
• C) $101100_2$
• D) $110001_2$

6. Convert $1_{10}$ to binary.

• A) $0_2$
• B) $1_2$
• C) $10_2$
• D) $11_2$

7. If you convert $30_{10}$ to binary, what is the result?

• A) $11100_2$
• B) $11110_2$
• C) $10110_2$
• D) $11010_2$