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Integers: excess/bias |
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One disadvantage of 2C: |
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Can't sort values just
using the bit representation. |
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Would look like negative
numbers were greater than positive numbers. |
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Another
idea: |
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Consider the unsigned
values for a 3-bit representation |
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representation |
value |
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excess-4 |
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000 |
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0 |
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-4 |
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001 |
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1 |
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-3 |
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010 |
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2 |
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-2 |
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011 |
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3 |
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-1 |
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100 |
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4 |
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0 |
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101 |
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5 |
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1 |
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110 |
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6 |
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2 |
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111 |
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7 |
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3 |
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Represent negative
values, but keep the values in representation order |
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First half of the
representations for negative, second half for positive |
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This is called excess, or
biased, representation. |
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Each value is shifted by
a constant amount; in this case the bias is 4. |
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Since there are 3 bits,
the bias value is 2(3-1) = 4 |
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In
general, for an N-bit representation, we will have half of the values
negative |
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and half of the values
non-negative if the bias is 2N-1. |
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However, the bias could
be any number < 2N -
2 |
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if the range of values
includes both positive and negative numbers. |
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Range of
values: N-bit excess K |
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Number of values: 2N |
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Minimum
negative value: -K |
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Maximum
positive value: 2N -1 - K |
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Converting base 10 to excess K |
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Add K
to the number |
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Convert to unsigned binary |
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Converting excess K to base 10 |
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Convert unsigned binary value to base 10 |
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Subtract K |
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Disadvantage: Can't use unsigned binary hardware to do addition. |
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Excess notation is used as part of floating point representation. |
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