What is the binary representation of the decimal number 164?

To convert a decimal number like 164 into its binary representation, we can use the method of successive division by 2 and noting the remainders.

Starting with 164, we divide it by 2 and keep track of the remainders:

1. 164 divided by 2 is 82, remainder 0

2. 82 divided by 2 is 41, remainder 0

3. 41 divided by 2 is 20, remainder 1

4. 20 divided by 2 is 10, remainder 0

5. 10 divided by 2 is 5, remainder 0

6. 5 divided by 2 is 2, remainder 1

7. 2 divided by 2 is 1, remainder 0

8. 1 divided by 2 is 0, remainder 1

Now, if we write down the remainders in reverse order (from the last division to the first), we get: 10100100.

This is the correct binary representation of 164. The breakdown shows clearly how each bit corresponds to a power of 2, contributing to the overall value of 164 in decimal form. Each '