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Published byJames Fountaine Modified over 2 years ago

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Excess Notation The other way to represent Integers.

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Excess Notation (examples are in 8 bits to save space) Fixed length notation system. Uses 0 to represent negative values. The largest non-negative value: The smallest non-negative value: The largest negative value is: The smallest negative value is:

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Excess Notation Consider the 8 patterns in 3 bits:

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Excess Notation Interpreted as Natural Numbers:

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Excess Notation Interpreted as Integers in 2s Complement:

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Excess Notation Interpreted as Integers in Excess Notation:

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Excess Notation Three different Interpretations:

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Excess Notation (examples are in 8 bits to save space) To better understand how binary patterns unpack under the 3 notations, lets look at an example. Consider the pattern Show the value represented if the pattern is: an unsigned integer an integer, in 2s Complement Notation an integer, in Excess Notation

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Excess Notation (examples are in 8 bits to save space) The pattern ( ) has 2 parts:

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Excess Notation (examples are in 8 bits to save space) The pattern ( ) has 2 parts: 1. the MSB

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Excess Notation (examples are in 8 bits to save space) The pattern ( ) has 2 parts: 1. the MSB 2. the rest

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Excess Notation (examples are in 8 bits to save space) The pattern ( ) has 2 parts: 1. the MSB 2. the rest Lets look at the rest:

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Excess Notation (examples are in 8 bits to save space) The pattern ( ) has 2 parts: 1. the MSB 2. the rest represents the Natural number = 57

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Excess Notation (examples are in 8 bits to save space) The pattern ( ) is, therefore, 57 greater than – regardless of the meaning of the MSB.

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Excess Notation (examples are in 8 bits to save space) As a Natural number, is 128

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Excess Notation (examples are in 8 bits to save space) As a Natural number, is 128 In 2s Complement, is the smallest, negative value… -128

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Excess Notation (examples are in 8 bits to save space) As a Natural number, is 128 In 2s Complement, is the smallest, negative value… -128 In Excess Notation, is the smallest, non-negative value… 0

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Excess Notation (examples are in 8 bits to save space) So the pattern is 57 greater than: 128 if its natural ( =185 ) -128 if its 2s Complement ( =-71 ) 0 if its Excess ( 57+ 0= 57 )

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