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Lecture 5

ITEC 1000 Lecture Notes - Lecture 5: Decimal Mark, Floating Point


Department
Information Technology
Course Code
ITEC 1000
Professor
Peter Khaiter
Lecture
5

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Lecture 5
1's 8-bit 11111111
2's 8-bit 100000000
SEEMMMMM
First digit represents the sign of mantissa
S (0) = "+"
5 = "-"
Two next digits(EE) represent exponent in excess-50
Five last digits(MMMMM) represent mantissa
fixed decimal point located at the beginning
Mantissa: stored in sign-magnitude format
Exponent: stored in Excess-N notation: Complementary notation
Pick middle value as offset where N is the middle value
0-99 e.g. excess -50
0 49 50 99
-50 -1 0 49
- Increasing magnitude +
Examples:
1. (+)0|52|43892 = 0.43892x102 = 43.892
52-50 = +2
2. (-)5|47|20100=-0.20100x10-3 = -0.000201
47-50 = -3
3. 5|56|78987 = -78987 x 106 = -789870
56-50 = 6
Excess-50 notation
Excess-N representation: R = N + EE
Example1: N = 50, EE = 38, R = 88
Example2: N = 50, EE = -38, R = 12
Excess-50: Magnitude range
4950 10 x 0.99999 number 10 x 00001.0 +±<<
Normalization
Shift numbers left by increasing the exponent until leading zeros eliminated
Converting decimal number into standard format
Examples:
1. 857.2601 x 100 -> 0.8572601 x 103 = 053857261
2. -0.00000075 x 100 -> 0.75 x 10-6 = 54475000
Floating Point Calculations
Addition and subtraction
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