1 1 0 0 1 0 1 0 1
28 27 26 25 24 23 22 21 20
Then, I wrote the 2 to the power of 0-8 starting from the right and listed them under each number, shown above. Then I took the number with the number 1 above it and took it to it's power and added them to get:
20=1 22=4 24=16 27=128 28=256
All equals 405. Therefore, (binary#) 110010101 = 405 (decimal#)
In order to convert a decimal number to a binary I take the number like 529 and divide it by 2. If there is a remainder of 1, then on the side write down a 1. If there is no remainder, then write down a 0 on the side. Therefore, this is what the process of converting 529 to binary looks like:
Decimal | Quotient | Remainder | Binary |
---|---|---|---|
529 | 264 | 1 | 1 |
264 | 132 | 0 | 01 |
132 | 66 | 0 | 001 |
66 | 33 | 0 | 0001 |
33 | 16 | 1 | 10001 |
16 | 8 | 0 | 010001 |
8 | 4 | 0 | 0010001 |
4 | 2 | 0 | 00010001 |
2 | 1 | 0 | 000010001 |
1 | 0 | 1 | 1000010001 |
As one can see the binary number for 529 is 1000010001.
Positional and Non-Positional Numbers
Positional numbers are numbers with a place value, for example decimal numbers. In order for the decimal number 529 to mean five hundred and twenty nine, the numbers have to be in a specific position. The number 9 is in the ones position, 2 is in the tens position, and the 5 is in the hundreds position. So when you add 9 ones + 2 tens + 5 hundreds = 9+20+500=529.
Non-Positional numbers are numbers that do not have a place values, for example, binary numbers do not have place values. 1000010001 = 529. The number 1000010001 has no place values, otherwise it means a totally different number. Therefore, the difference between positional and non-positional numbers is that postitional number has place values and the other does not.