Download presentation

1
**The other way to represent Integers.**

Excess Notation The other way to represent Integers.

2
**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:

3
**Excess Notation 111 110 Consider the 8 patterns in 3 bits: 101 100 011**

010 001 000

4
**Excess Notation Interpreted as Natural Numbers: 111 7 110 6 101 5 100**

4 011 3 010 2 001 1 000

5
**Excess Notation Interpreted as Integers in 2’s Complement: 111 -1 110**

-2 101 -3 100 -4 011 3 010 2 001 1 000

6
**Excess Notation Interpreted as Integers in Excess Notation: 111 3 110**

2 101 1 100 011 -1 010 -2 001 -3 000 -4

7
**Excess Notation Three different Interpretations: 111 7 -1 3 110 6 -2 2**

101 5 -3 1 100 4 -4 011 010 001 000

8
**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 Show the value represented if the pattern is: an unsigned integer an integer, in 2’s Complement Notation an integer, in Excess Notation

9
**Excess Notation (examples are in 8 bits to save space)**

The pattern ( ) has 2 parts:

10
**Excess Notation (examples are in 8 bits to save space)**

The pattern ( ) has 2 parts: the MSB

11
**Excess Notation (examples are in 8 bits to save space)**

The pattern ( ) has 2 parts: the MSB the rest

12
**Excess Notation (examples are in 8 bits to save space)**

The pattern ( ) has 2 parts: the MSB the rest Let’s look at the “rest”:

13
**Excess Notation (examples are in 8 bits to save space)**

The pattern ( ) has 2 parts: the MSB the rest represents the Natural number = 57

14
**Excess Notation (examples are in 8 bits to save space)**

The pattern ( ) is, therefore, 57 greater than – regardless of the meaning of the MSB.

15
**Excess Notation (examples are in 8 bits to save space)**

As a Natural number, is 128

16
**Excess Notation (examples are in 8 bits to save space)**

As a Natural number, is 128 In 2’s Complement, is the smallest, negative value…

17
**Excess Notation (examples are in 8 bits to save space)**

As a Natural number, is 128 In 2’s Complement, is the smallest, negative value… In Excess Notation, is the smallest, non-negative value…

18
**Excess Notation (examples are in 8 bits to save space)**

So the pattern 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)

Similar presentations

Presentation is loading. Please wait....

OK

Recursion and Induction

Recursion and Induction

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on 2nd world war records Ppt on formal education system Ppt on environmental protection act 1986 Ppt on zener diode operation Ppt on online art gallery Ppt on db2 mainframes ibm Ppt on global warming in hindi Ppt on marie curie's husband Ppt on k-map simplification Ppt on division as equal sharing