Appendix E Number Systems (on CD) 1359 For (Web server)
Appendix E Number Systems (on CD) 1359 For longer decimal numbers, the next positions to the left would be the thousands position (10 to the 3rd power), the ten-thousands position (10 to the 4th power), the hundred- thousands position (10 to the 5th power), the millions position (10 to the 6th power), the ten-millions position (10 to the 7th power), and so on. In the binary number 101, we say that the rightmost 1 is written in the ones position, the 0 is written in the twos position, and the leftmost 1 is written in the fours position. Notice that each of these positions is a power of the base (base 2), and that these powers begin at 0 and increase by 1 as we move left in the number (Fig E.4). For longer binary numbers, the next positions to the left would be the eights position (2 to the 3rd power), the sixteens position (2 to the 4th power), the thirty-twos position (2 to the 5th power), the sixty-fours position (2 to the 6th power), and so on. In the octal number 425, we say that the 5 is written in the ones position, the 2 is written in the eights position, and the 4 is written in the sixty-fours position. Notice that each of these positions is a power of the base (base 
, and that these powers begin at 0 and increase by 1 as we move left in the number (Fig. E.5). For longer octal numbers, the next positions to the left would be the five-hundred-andtwelves position (8 to the 3rd power), the four-thousand-and-ninety-sixes position (8 to the 4th power), the thirty-two-thousand-seven-hundred-and-sixty eights position (8 to the 5th power), and so on. In the hexadecimal number 3DA, we say that the A is written in the ones position, the D is written in the sixteens position, and the 3 is written in the two-hundred-and-fifty-sixes position. Notice that each of these positions is a power of the base (base 16), and that these powers begin at 0 and increase by 1 as we move left in the number (Fig. E.6). Positional values in the binary number system Binary digit 1 0 1 Position name Fours Twos Ones Positional value 4 2 1 Positional value as a 22 21 20 power of the base (2) Fig. E.4Fig. Positional values in the binary number system. Positional values in the octal number system Decimal digit 4 2 5 Position name Sixty-fours Eights Ones Positional value 64 8 1 Positional value as a 82 81 80 power of the base (8) Fig. E.5Fig. Positional values in the octal number system.
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