1278 Number Systems Appendix B Attribute Binary Octal (Web hosting ecommerce)
1278 Number Systems Appendix B Attribute Binary Octal Decimal Hexadecimal Base 2 8 10 16 Lowest digit 0000 Highest digit 179F Fig. B.2 Comparison of the binary, octal, decimal and hexadecimal number systems. Positional values in the decimal number system Decimal digit 9 3 7 Position name Hundreds Tens Ones Positional value 100 10 1 Positional value as a 102 101 100 power of the base (10) Fig. B.3 Positional values in the decimal number system. 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. B.6). For longer hexadecimal numbers, the next positions to the left would be the four-thousand- and-ninety-sixes position (16 to the 3rd power), the sixty-five-thousand-five-hundred- and-thirty-six position (16 to the 4th power), and so on. 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 power of the base (2) 22 21 20 Fig. B.4 Positional values in the binary number system.
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