To convert the decimal number $511$ to its binary equivalent, follow these steps:

1. Find the highest power of 2 less than or equal to 511. The highest power is $2^8 = 256$.

2. Subtract this value from 511: $511 - 256 = 255$

3. Repeat the process for the remainder (255) using the next lower powers of 2:

   • $2^7 = 128$: $255 - 128 = 127$
   • $2^6 = 64$: $127 - 64 = 63$
   • $2^5 = 32$: $63 - 32 = 31$
   • $2^4 = 16$: $31 - 16 = 15$
   • $2^3 = 8$: $15 - 8 = 7$
   • $2^2 = 4$: $7 - 4 = 3$
   • $2^1 = 2$: $3 - 2 = 1$
   • $2^0 = 1$: $1 - 1 = 0$

4. Write the binary equivalent by placing a 1 in the positions corresponding to the powers of 2 that were subtracted, and 0 in all other positions. Since all powers from $2^8$ down to $2^0$ were used, the binary representation is:

$\text{Binary equivalent of } 511 = 111111111_2$

Would you like more details or have any questions? Here are some related questions:

1. How to convert a larger decimal number to binary?
2. How to convert binary numbers back to decimal?
3. What is the binary equivalent of 1023?
4. How to convert fractional decimal numbers to binary?
5. What is the importance of binary numbers in computing?

Tip: The binary number system is fundamental in computing as it directly represents the on/off state of transistors in digital circuits.