Converting Numbers

Converting Binary Numbers to Decimal Numbers and Back

Convert 110010101 to Decimal

This number has nine places in it. This means you have to go from 2^0-2^8. Then you multiply either the 0 or 1 to what ever 2^n it is. Then you add up all of those numbers.

(2^8 * 1) + (2^7 *1) + (2^6 * 0) + (2^5 * 0) + (2^4 * 1) + (2^3 * 0) + (2^2 * 1) + (2^1 * 0) + (2^0 * 1) = Decimal Number

256 + 128 + 0 + 0 + 16 + 0 + 4 + 0 + 1 = 405



Convert 529 to Binary

To convert to binary you keep dividing the number until you get to 0. You use the remandiers for the binary number.

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

1 0 1 1100010001


A positonal number system has places for numbers and 0's for spots where there is not a number. The decimal system is a good example. There are specific places for numbers. There is the 1's, 10's 100's 1,000's.......places. There is also the 10ths, 100ths, 1,000ths......places. The numbers are added together as you see them. 1,056= 1,000+50+6.

A non-positional number system does not use 0's for spots where there are no numbers. The Roman numerical system is a good example. For 1 there is I. For 2, II. For 3, III. For 5, V. To get for you put the symbol for 1 before the symbol for 5, IV. 10, X. For 9, IX. To get 11, you put the symbol for 1 after the X, XI. To get 101 there is not a symbol that represents 0. C represents 100, CI represents 101.