10 equals 2?
...0, which really means “1 ten plus no ones.” The next number is 11, or “1 ten plus 1 one”. After we get to the number 99, then we have to put a 1 in the next column, the “hundreds place”, and we get 100, or “1 hundred and no tens and no ones.” Numbers written using this method (the way we normally write them) are called “decimal” numbers. The first column is the ones place. Then comes the tens place, hundreds place, and so on. We will call these values (1, 10, 100, …) “place values.” Figure 1 shows a couple of examples of decimal numbers. As shown, to get the value of a decimal number, you multiply each digit by its place value. 100 10 1 327 = 3 100 + 2 10 + 7 1 283 = 2 100 + 8 10 + 3 1 Figure 1. Examples of Decimal Numbers. Binary Numbers But, what if there were aliens with only two fingers? Then they would only use two digits, like 0 and 1. They would start counting 0 and then 1, but what comes after 1? They would do what we do, put a 1 in the next column. Instead of the “tens place”, the next column is called the “twos place.” So after 1 comes 10, which means “1 two and no ones.” If we add one to that, we get “1 two plus 1 one”, or 11, which equals 3. We’ve run out of digits again so, to get to the next number, we put a 1 in the next column—the “fours place”. This gives us 100, or “1 four and no twos and no ones.” Figure 2 shows how to count to 15 in binary. 8 4 2 1 0 = 0 1 = 0 1 = 1 1 = 1 10 = 1 2 + 0 1 = 2 11 = 1 2 + 1 1 = 3 100 = 1 4 + 0 2 + 0 1 = 4 101 = 1 4 + 0 2 + 1 1 = 5 110 = 1 4 + 1 2 + 0 1 = 6 111 = 1 4 + 1 2 + 1 1 = 7 1000 = 1 8 + 0 4 + 0 2 + 0 1 = 8 1001 = 1 8 + 0 4 + 0 2 + 1 1 = 9 1010 = 1 8 + 0 4 + 1 2 + 0 1 = 10 1011 = 1 8 + 0 4 + 1 2 + 1 1 = 11 1100 = 1 8 + 1 4 + 0 2 + 0 1 = 12 1101 = 1 8 + 1 4 + 0 2 + 1 1 = 13 1110 = 1 8 + 1 4 + 1 2 + 0 1 = 14 1111 = 1 8 + 1 4 + 1 2 + 1 1 = 15 Figure 2. Converting From Binary to Decimal. 106 105 104 1,000 =103 100 = 102 10 = 101 1 = 100 a) Decimal Numbers: Each column has ten times the value of the column to the right. 64 = 26 32 = 25 16 = 24 8 = 23 4 = 22 2 = 21 1 = 20 b) Binary Numbers: Each column has twice the value of the column to the rig...