GT AE 6382 - Numeric Representation in a Computer (28 pages)

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Numeric Representation in a Computer



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Numeric Representation in a Computer

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Lecture Notes


Pages:
28
School:
Georgia Institute of Technology
Course:
Ae 6382 - Computing Sys Engr Lab

Unformatted text preview:

Numeric Representation in a Computer Learning Objectives Understand how numbers are stored in a computer and how the computer operates on them AE6382 Design Computing Topics Numbers on a computer Precision and accuracy Numeric operators Precedence Exercises Summary 1 Fall 2006 Numbers precision and accuracy Good Accuracy Good Precision Good Precision Poor Accuracy Good Accuracy Poor Precision Poor Accuracy Poor Precision Low precision 3 14 High precision 3 140101011 Low accuracy 3 10212 High accuracy 3 14159 High accuracy precision 3 141592653 AE6382 Design Computing 2 Fall 2006 Computer Memory Numbers and the results of numeric computations along with other data such as text graphics documents etc must be stored somewhere in a computer That somewhere is memory Memory comes in a variety of types and speeds Cache in the CPU itself fastest RAM external to the CPU fast Disk physical media external to the CPU r w CDROM physical media slow Tape physical media slowest Memory is measured in bytes and kilobytes megabytes gigabytes and terabytes AE6382 Design Computing 3 Fall 2006 Computer Memory is Varied AE6382 Design Computing 4 Fall 2006 Memory in MATLAB AE6382 Design Computing 5 Fall 2006 Inside the Bytes In the previous slide we see Name Size Bytes Class k 1x1 8 s 1x12 24 x 1x200 1600 double array char array double array Grand total is 213 elements using 1632 bytes What is the size of the variable i What does class represent How many bytes are used to store the value AE6382 Design Computing 6 Fall 2006 Numbers and their Bases Numbers we use are DECIMAL or base 10 Digits 0 1 2 3 4 5 6 7 8 9 123 1 102 2 101 3 100 But we can always use other bases Octal base 8 Digits 0 1 2 3 4 5 6 7 123 1 82 2 81 3 80 1238 64 16 3 8310 Binary base 2 Digits 0 1 1011 1 23 0 22 1 21 1 20 10112 8 0 2 1 1110 1238 001 010 011 10100112 Hexidecimal base 16 Digits 0 1 2 3 4 5 6 7 8 9 A B C D E F 123 1 162 2 161 3 160 12316 256 32 3 29110 12316 0001 0010 0011 1001000112 AE6382 Design Computing 7



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