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Week of November 12 - Class notes for the week of November...

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Class notes for the week of November 12 th Number representations: We are all very familiar with the decimal system, it this lecture we will expand on this knowledge and learn how to express integer quantities in other number bases that offer advantages for use in digital systems. The decimal integer quantity 3581 can be written as: This last form is the most germane for our purpose. Each column of numbers is multiplied by a power of 10 which starts at 10 0 in the right hand column, then 10 1 for the next column to the left, and so on increasing by a factor of ten for each column. These concepts are deeply embedded in our language, and we call the columns the ones column, the tens column, the hundreds column and so on. Other number bases work the same way, except that the base for the exponent is not 10 but some other number. In the binary system the base is 2. the rightmost column is therefore 2 0 , then the next column to the left is 2 1 , then 2 2 , and so on. The table below shows some powers of 2 and their decimal equivalents. Power of two 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 Decimal equivalent 12 8 6 4 3 2 1 6 8 4 2 1 We construct a binary number in the same way as a decimal number. The binary number 01101101 is equivalent to 0*2 7 + 1*2 6 + 1*2 5 + 0*2 4 + 1*2 3 + 1*2 2 + 0*2 1 + 1*2 0 . We can
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