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Biased Representation

Shift all values by subtracting a bias from the unsigned interpretation.

The unsigned representation for the bias value, B, becomes the 0 value in biased representation.

Bias values begin at -B and increase in the direction of the 0 value.

The integer represented by an (n+1) bit biased-B representation is:

displaymath330

The range of values for an (n+1) bit biased-B representation is from -B to tex2html_wrap_inline332

The bias value, B, is usually tex2html_wrap_inline334 or tex2html_wrap_inline310 for an (n+1) bit representation, which gives a range of values from approximately tex2html_wrap_inline324 to tex2html_wrap_inline340 .

For example, a three bit biased representation with B = tex2html_wrap_inline342 = 4 is:

tabular136

For an 8 bit biased representation, the bias would be either 127 or 128 and the range of values would be approximately -128 to +128.

When the bias equals tex2html_wrap_inline334 or tex2html_wrap_inline310 , the leftmost bit indicates the sign of the number, but is inverted from the sign-magnitude and complement representations.

Negative bias values precede the 0 value with leftmost bit = 0, while positive bias values follow the 0 value with the leftmost bit = 1.



CS 301 Class Account
Mon Sep 14 23:38:35 ADT 1998