The binary representation of the decimal number $53$ is $110101$.

To convert a decimal number to binary, we employ a systematic method of repeatedly dividing the number by $2$ and recording the remainders. Let’s explore the conversion of the decimal number $53$ into its binary form step by step.

1. Divide $53$ by $2$:
   The quotient is $26$ and the remainder is $1$. This remainder becomes the least significant bit (the rightmost bit) of the binary representation.

2. Divide the quotient $26$ by $2$:
   The new quotient is $13$ and the remainder is $0$. This remainder is the next bit to the left in the binary sequence.

3. Divide the quotient $13$ by $2$:
   This division yields a quotient of $6$ and a remainder of $1$. This remainder represents the next bit in the binary format.

4. Divide $6$ by $2$:
   The result is a quotient of $3$ and a remainder of $0$. This remainder is added as the next bit.

5. Divide $3$ by $2$:
   Here, the quotient is $1$ and the remainder is $1$. Both the quotient and the remainder contribute to the binary representation.

6. Finally, divide the last quotient $1$ by $2$:
   The quotient is $0$ and the remainder is $1$. This remainder becomes the most significant bit (the leftmost bit).

Now, if we compile all the remainders from the last step to the first, we obtain $110101$. Thus, the binary representation of the decimal number $53$ is $110101$.