If the decimal number 15 is converted to binary, what is the resulting binary nu

If the decimal number 15 is converted to binary, what is the resulting binary number?

If the decimal number 15 is converted to binary, what is the resulting binary number?

Step 1: Understand that binary is a base-2 number system, which uses only two digits: 0 and 1.
Step 2: Start with the decimal number 15.
Step 3: Find the largest power of 2 that is less than or equal to 15. The powers of 2 are 1, 2, 4, 8, 16. The largest power of 2 less than 15 is 8 (which is 2^3).
Step 4: Subtract 8 from 15. This gives you 7.
Step 5: Find the largest power of 2 less than or equal to 7. This is 4 (which is 2^2).
Step 6: Subtract 4 from 7. This gives you 3.
Step 7: Find the largest power of 2 less than or equal to 3. This is 2 (which is 2^1).
Step 8: Subtract 2 from 3. This gives you 1.
Step 9: The largest power of 2 less than or equal to 1 is 1 (which is 2^0).
Step 10: Subtract 1 from 1. This gives you 0.
Step 11: Now, we have used the powers of 2: 8, 4, 2, and 1. In binary, this means we have 1 for each of these powers and 0 for any powers of 2 we did not use.
Step 12: Write down the binary representation: 1 (for 8), 1 (for 4), 1 (for 2), and 1 (for 1). This gives us 1111.

Decimal to Binary Conversion – Understanding how to convert a decimal number into its binary equivalent using division by 2 or by recognizing binary patterns.