Lab 6

Below is the procedure needed to convert the binary number 110010101 into the decimal number 405:

1 1 0 0 1 0 1 0 1

2^8 2^7 2^4 2^2 2^0

256 + 128 + 16 + 4 + 1 = 405

Below is how to convert the decimal number 529 into they binary number 100010001:

Decimal Quotient Remain 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 1 100010001

In a positional number system the value of each digit is determined by its position. For example we use n as the base for our number system. For any number in this system each digit to the left is equal to n times the position to the right; each each digit to the right is equal to the position to the left divided by n. The decimal system is an example of a positional number system with the base of 10.

Non-positional number systems' numbers can be represented by different symbols. The Roman number system is an example because each numeral in the system represent each level of magnitude by a different symbol.