Excess Notation

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## Excess Notation

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**Excess Notation**The other way to represent Integers.**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: 11111111 The smallest non-negative value: 10000000 The largest negative value is: 01111111 The smallest negative value is: 00000000**Excess Notation**Consider the 8 patterns in 3 bits:**Excess Notation**Interpreted as Natural Numbers:**Excess Notation**Interpreted as Integers in 2’s Complement:**Excess Notation**Interpreted as Integers in Excess Notation:**Excess Notation**Three different Interpretations:**Excess Notation(examples are in 8 bits to save space)**To better understand how binary patterns unpack under the 3 notations, let’s look at an example. Consider the pattern 10111001 Show the value represented if the pattern is: • an unsigned integer • an integer, in 2’s Complement Notation • an integer, in Excess Notation**Excess Notation(examples are in 8 bits to save space)**The pattern (10111001) has 2 parts:**Excess Notation(examples are in 8 bits to save space)**The pattern (10111001) has 2 parts: • the MSB**Excess Notation(examples are in 8 bits to save space)**The pattern (10111001) has 2 parts: • the MSB • the rest**Excess Notation(examples are in 8 bits to save space)**The pattern (10111001) has 2 parts: • the MSB • the rest Let’s look at the “rest”: 0111001**Excess Notation(examples are in 8 bits to save space)**The pattern (10111001) has 2 parts: • the MSB • the rest 0111001 represents the Natural number32 + 16 + 8 + 1= 57**Excess Notation(examples are in 8 bits to save space)**The pattern (10111001) is, therefore, 57 greater than10000000– regardless of the meaning of the MSB.**Excess Notation(examples are in 8 bits to save space)**As a Natural number,10000000 is 128**Excess Notation(examples are in 8 bits to save space)**As a Natural number,10000000 is 128 In 2’s Complement,10000000 isthe smallest, negative value… -128**Excess Notation(examples are in 8 bits to save space)**As a Natural number,10000000 is 128 In 2’s Complement,10000000 isthe smallest, negative value… -128 In Excess Notation,10000000 isthe smallest, non-negative value… 0**Excess Notation(examples are in 8 bits to save space)**So the pattern 10111001 is 57 greater than: 128 if it’s natural (57+128=185) -128 if it’s 2’s Complement (57-128=-71) 0 if it’s Excess (57+ 0= 57)