Representing Data - Representing Data The information below...

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Representing Data The information below is provided to help you review and practice converting numbers. Binary numbers are expressed in a positional notation system. Each digit represents a power of 2. In an 8-bit pattern the column positions have these digit values: 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 0 128 64 32 16 8 4 2 1 For example, the number 11111111 expresses the highest magnitude an 8-bit pattern can represent (128+64+32+16+8+4+2+1 = 255) which is exactly 1 less than the digit value of the next column which is 256 Binary Fractions (radix point) the radix point . separates integers from fractions fraction digits inversely mirror the values of the integers: .1/2 1/4 1/8 1/16 1/32 1/64 1/128 ... 1011.1100 converts to 8 + 0 + 2 + 1 + 1 / 2 + 1 / 4 + 0 + 0 = 11 3 / 4 Hexadecimal notation is a short hand for representing a 4 bit pattern using only a single character (a base 16 digit.)
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Excess notation makes it possible to store negative values by treating the Most Significant Bit (MSB) as the sign. In excess notation a 0 as the MSB indicates a negative (-) number. This system requires a fixed number of bits at the outset.
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This note was uploaded on 11/16/2010 for the course NATURAL SC NATS 1505 taught by Professor Isley during the Spring '10 term at Columbia State Community College.

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Representing Data - Representing Data The information below...

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