What is the binary representation of the decimal number 784?

The binary representation of the decimal number 784 is 1100010000.

To convert a decimal number to binary, we use a process of dividing by 2 and tracking the remainders. Starting with the number 784, we divide by 2 to get 392 with a remainder of 0. This remainder is the least significant bit (rightmost bit) of our binary number. We then continue this process with the quotient (392), again dividing by 2 to get 196 with a remainder of 0. This gives us the next bit of our binary number.

Continuing this process, we get the following sequence of quotients and remainders:

784 / 2 = 392 remainder 0 (least significant bit)
392 / 2 = 196 remainder 0
196 / 2 = 98 remainder 0
98 / 2 = 49 remainder 0
49 / 2 = 24 remainder 1
24 / 2 = 12 remainder 0
12 / 2 = 6 remainder 0
6 / 2 = 3 remainder 0
3 / 2 = 1 remainder 1
1 / 2 = 0 remainder 1 (most significant bit)

Reading the remainders from bottom to top gives us the binary representation of 784: 1100010000.

This method of converting decimal to binary is known as the 'division by 2' algorithm. It's a simple and effective way to understand how decimal numbers can be represented in binary, which is fundamental to how data is stored and processed in computers. It's also a great example of how a seemingly complex process can be broken down into a series of simple steps, a key skill in computer science.