W5Lect - Numbering Systems Math and Conversion Decimal...

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Numbering Systems Math and Conversion Decimal Octal Hexadecimal Binary
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Conversion When does When does 5 5 * * 8 = 8 = Or Or 0101 0101 * * 1000 = 1000 = 50 50 28 28 40 40 101000 101000
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Decimal system the decimal number system we use every day is built on base ten it is based on 10 positions numbered 0 thru 9 each position corresponds to a power of 10 1024 is: 2 x 10 = 20 4 x 1 = 4
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Decimal Numbers The easiest way to understand bits is to compare them to something you know: digits A digit is a single place that can hold numerical values between 0 and 9. Digits are normally combined together in groups to create larger numbers. For example, 6,357 has four digits. It is understood that in the number 6,357, the 7 is filling the "1s place," while the 5 is filling the 10s place, the 3 is filling the 100s place and the 6 is filling the 1,000s place. So you could express things this way if you wanted to be explicit: (6 * 1000) + (3 * 100) + (5 * 10) + (7 * 1) = 6000 + 300 + 50 + 7 = 6357 powers of 10. Assuming that we are going to represent the concept of "raised to the power of" with the "^" symbol (so "10 squared" is written as "10^2"), another way to express it is like this: (6 * 10^3) + (3 * 10^2) + (5 * 10^1) + (7 * 10^0) = 6000 + 300 + 50 + 7 = 6357
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Binary system computer memory is based on the electrical representation of data each memory position is represented by a bit which can be either 'on' or 'off'. This makes it easier to represent computer memory using a base 2 number system rather than the base 10 decimal system. Binary system represents numbers by a series of 1's and 0's. a 1 represents an 'on' position a 0, an 'off' position a hex byte is represented by 8 bits numbered 0 to 7 from left to right the leftmost bit is called the high-order bit, the right most bit, the low- order bit.
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Bytes (Hexadecimal) Bits are rarely seen alone in computers. They are almost always bundled together into 8-bit collections, and these collections are called bytes. Why are there 8 bits in a byte? The 8-bit byte is the MOST efficient way to use memory each bit in a byte (2 hexadecimal characters) is used. With 8 bits in a byte, you can represent 256 values ranging from 0 to 255, as shown here: 0 = 00000000 1 = 00000001 2 = 00000010 ………. . 254 = 11111110 255 = 11111111
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BINARY uses base 2 Each binary digit is represented by 1 bit An binary byte equals 1 bit Binary digits are represented by 0 thru 1 each position is a power of 2 used inside the computer and expressed as “ON or OFF”
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Octal uses base 8 Each octal digit is represented by 3 bits An octal byte equals 6 bits octal digits are represented by 0 thru 7 each position is a power of 8 Rarely seen today – only used for specific purposes ( network addressing, permissions in Unix, ,,,,)
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This note was uploaded on 05/17/2010 for the course CTY HWD101 taught by Professor Parker during the Winter '10 term at Seneca.

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W5Lect - Numbering Systems Math and Conversion Decimal...

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