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Lecture 5

lecture 5.docx

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Department
Information Technology
Course Code
ITEC 1000
Professor
Peter Khaiter

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Description
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 = 0.43892x10 = 43.892 52-50 = +2 2. (-)5|47|20100=-0.20100x10 = -0.000201 47-50 = -3 6 3. 5|56|78987 = -78987 x 10 = -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 0.00001x10 −5< number <0.99999 x ±10 +49 Normalization Shift numbers left by increasing the exponent until leading zeros eliminated Converting decimal number into standard format Examples: 0 3 1. 857.2601 x 10 -> 0.8572601 x 10 = 053857261 2. -0.00000075 x 10 -> 0.75 x 10 = 54475000 Floating Point Calculations Addition and subtraction Exponent and mantissa treated separately Examples: 1. Add 2 floating point numbers 05199520 + 04967850 Align exponents 05199520 0510067850 Add mantissas; (1) indicates a carry (1)0
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