To convert the decimal number 63 to binary (base 2), we repeatedly divide by 2, recording the remainders:

1. $63 \div 2 = 31$ remainder 1
2. $31 \div 2 = 15$ remainder 1
3. $15 \div 2 = 7$ remainder 1
4. $7 \div 2 = 3$ remainder 1
5. $3 \div 2 = 1$ remainder 1
6. $1 \div 2 = 0$ remainder 1

Now, we take the remainders from bottom to top: 111111.

Thus, 63 in base 2 is 111111.

Would you like further explanation or help with anything else? Here are a few related questions for you:

1. How would you convert the number 45 to binary?
2. What is the relationship between binary and hexadecimal?
3. How do you convert from binary back to decimal?
4. What is the significance of binary numbers in computer science?
5. How can you convert a binary number to octal?

Tip: To convert any decimal number to binary, divide by 2 and keep track of the remainders. The binary number is formed by reading the remainders from bottom to top!