1 / 18

221 likes | 597 Vues

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

Télécharger la présentation
## Excess Notation

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**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)

More Related