Explain how you would convert a decimal to a binary number. What is the significance of the resulting binary number in computer systems?

Converting a decimal number to a binary number involves the following steps:

1. Divide the decimal number by 2.
2. Record the remainder.
3. Divide the quotient from the previous step by 2.
4. Repeat steps 2 and 3 until you reach a quotient of zero.
5. The binary number is the sequence of remainders read in reverse order.

For example, if you want to convert the decimal number 10 to binary:

1. 10 divided by 2 equals 5, remainder 0.
2. 5 divided by 2 equals 2, remainder 1.
3. 2 divided by 2 equals 1, remainder 0.
4. 1 divided by 2 equals 0, remainder 1.
5. Reading the remainders in reverse order gives you 1010, which is the binary equivalent of the decimal number 10.

In computer systems, binary numbers are significant because they are used in digital circuits and systems. Computers use the binary number system, also known as base 2, because it's easier and more cost-effective to build systems that only need to distinguish between two electrical states - on and off, or high voltage and low voltage. These two states represent the 0s and 1s in binary.