The problem asks to convert the decimal number 77 (written as $77_{10}$) into its binary (base 2) equivalent.

To convert from decimal to binary, we can divide the number by 2 repeatedly and keep track of the remainders:

1. $77 \div 2 = 38$ with remainder $1$
2. $38 \div 2 = 19$ with remainder $0$
3. $19 \div 2 = 9$ with remainder $1$
4. $9 \div 2 = 4$ with remainder $1$
5. $4 \div 2 = 2$ with remainder $0$
6. $2 \div 2 = 1$ with remainder $0$
7. $1 \div 2 = 0$ with remainder $1$

Now, writing the remainders from bottom to top gives the binary number: $1001101_2$.

Thus, $77_{10} = 1001101_2$.

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. Convert $45_{10}$ to binary.
2. What is $1001011_2$ in decimal?
3. Convert $100011_2$ to decimal.
4. What is the binary representation of $128_{10}$?
5. How do you convert a binary fraction like $1101.01_2$ to decimal?

Tip: When converting from decimal to binary, always divide by 2 and track remainders from last to first!