To find the binary equivalent of the decimal number 13, we will convert the decimal number into binary using the method of successive division by 2. Let's go through the steps in detail. ### Step-by-Step Conversion from Decimal to Binary 1. **Understanding Binary System**: - The binary system is a base-2 numeral system that uses only two digits: 0 and 1. Each digit represents a power of 2, starting from \(2^0\) on the right. 2. **Division by 2**: - We will divide the decimal number (13) by 2 and keep track of the quotient and the remainder. The remainder will give us the binary digits. 3. **Performing the Division**: - **First Division**: - \(13 \div 2 = 6\) with a remainder of \(1\). - **Second Division**: - \(6 \div 2 = 3\) with a remainder of \(0\). - **Third Division**: - \(3 \div 2 = 1\) with a remainder of \(1\). - **Fourth Division**: - \(1 \div 2 = 0\) with a remainder of \(1\). 4. **Collecting the Remainders**: - Now, we collect the remainders from the last division to the first: - The remainders are: \(1\) (from the fourth division), \(1\) (from the third division), \(0\) (from the second division), and \(1\) (from the first division). - Reading these from bottom to top gives us \(1101\). 5. **Final Binary Representation**: - Therefore, the binary equivalent of the decimal number 13 is **1101**. ### Conclusion The correct option is **B. 1101**. ### Explanation of Other Options - **A. 1100**: This represents the decimal number 12. The binary digits correspond to \(1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0 = 8 + 4 + 0 + 0 = 12\). - **C. 1011**: This represents the decimal number 11. The binary digits correspond to \(1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 8 + 0 + 2 + 1 = 11\). - **D. 1110**: This represents the decimal number 14. The binary digits correspond to \(1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 8 + 4 + 2 + 0 = 14\). ### Common Pitfalls - **Miscounting Remainders**: Ensure you collect the remainders in the correct order (from last to first). - **Confusing Binary with Decimal**: Remember that binary uses only 0s and 1s, and each position represents a power of 2. ### Revision Summary - The binary equivalent of decimal 13 is **1101**. - Use successive division by 2 to convert decimal to binary. - Collect remainders from the last division to the first. - Be careful with the order of remainders and ensure you understand the binary system.