Question

What is the binary base 2 representation of the decimal number 255?

Answer 1

To convert the decimal number 255 into its binary base 2 representation, we can continuously divide the number by 2 and record the remainders. Here’s how it works:

1. 255 divided by 2 equals 127 with a remainder of 1.
2. 127 divided by 2 equals 63 with a remainder of 1.
3. 63 divided by 2 equals 31 with a remainder of 1.
4. 31 divided by 2 equals 15 with a remainder of 1.
5. 15 divided by 2 equals 7 with a remainder of 1.
6. 7 divided by 2 equals 3 with a remainder of 1.
7. 3 divided by 2 equals 1 with a remainder of 1.
8. 1 divided by 2 equals 0 with a remainder of 1.

Now, we take the remainders from the last division to the first, which gives us:

1, 1, 1, 1, 1, 1, 1, 1

Thus, the binary representation of 255 is:

**11111111**