COMPUTER 2430 Object Oriented Programming and Data Structures I

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Presentation transcript:

COMPUTER 2430 Object Oriented Programming and Data Structures I

Fixed Point Numbers Prog2 Computers need to perform floating point calculations Microprocessor chosen doesn't have a floating point capability

We use two integers to represent a double number. Fixed Point Numbers We use two integers to represent a double number. intVal qVal

How to Store Integers in Computer Binary Number 27 26 25 24 23 22 21 20 1 27 + 23 + 22 + 21 + 20 + 8 + 4 + 2 + 1 Decimal Number: 143

How to Store Signed Integers Binary Number 26 25 24 23 22 21 20 Sign bit 1 - 23 + 22 + 21 + 20 - 8 + 4 + 2 + 1 Decimal Number: -15

How to Store Signed Integers Binary Number 26 25 24 23 22 21 20 Sign bit 1 + 23 + 22 + 21 + 20 + 8 + 4 + 2 + 1 Decimal Number: +15

Prog2 Integers are 4 bytes, 32 bits We only consider positive numbers and ignore the sign

How to Store Positive Float Numbers 25 24 23 22 21 20 2-1 2-2 Implicit binary point qVal: 2 Fixed Point Number: intVal qVal

How to Store Positive Float Numbers Implicit Binary Point : qVal = 2 25 24 23 22 21 20 2-1 2-2 1 25 + 21 + 20 + 2-1 + 2-2 32 + 2 + 1 + 0.5 + 0.25 Decimal Number: 35.75

How to Store Positive Float Numbers Implicit Binary Point : qVal = 2 25 24 23 22 21 20 2-1 2-2 Decimal Number: 35.7512 35.7512 * 22 = 143.0048 = 143 1 143.0 / 22 = 35.75

Double to FixedPoint intVal = (int)(dbl * Math.pow(2, qVal)) Choose your qVal Different qVal values store the same double number with different precisions

FixedPoint to Double intVal = (int)(dbl * Math.pow(2, qVal)) dbl = intVal / Math.pow(2, qVal) You may not get the original double number!

How to Store Positive Float Numbers Fixed Point Number: qVal = 4 23 22 21 20 2-1 2-2 2-3 2-4 1 23 + 2-1 + 2-2 + 2-3 + 2-4 8 + .5 + .25 + 0.125 + 0.0625 Decimal Number: 8.9375

How to Store Float Numbers in Computer Fixed Point Number: qVal = 4 23 22 21 20 2-1 2-2 2-3 2-4 Decimal Number: 8.937567 8.937567 * 24 = 143.001072 = 143 1 143.0 / 24 = 8.9375

How to Store Data in Computer 1 Char: ? Integer 143 Fixed Point Number: qVal = 4 8.9375 Fixed Point Number: qVal = 2 37.75

Shift Operator 1 x: 40 x >> 2 New value: 10 (40 / 22 ) 1 1 x: 40 x >> 2 New value: 10 (40 / 22 ) 1 x << 2 New value: 160 (40 * 22 ) 1

Shift Operator 1 x: 40 x >> 4 New value: 2 (Underflow) 1 1 x: 40 x >> 4 New value: 2 (Underflow) 1 x << 4 New value: 128 (Overflow) 1

Prog2 We ignore overflows Underflows are not totally ignored

Shift Operator 1 x: 40 x >> -2 New value: 0 x << -2 1 x: 40 x >> -2 New value: 0 x << -2 Don’t do it!

Change qVal 1 dbl: 8.9375 Fixed Point Number: dbl * 24 dbl: 8.9375 Fixed Point Number: dbl * 24 qVal: 4, intVal: 143 Change qVal to 2: dbl * 22 (but we don’t have the original dbl any more!) intVal = intVal >> 2 8.75 (underflow) 1

Change qVal 1 dbl: 2.9375 Fixed Point Number: dbl * 24 1 dbl: 2.9375 Fixed Point Number: dbl * 24 qVal: 4, intVal: 47 Change qVal to 6: dbl * 26 intVal = intVal << 2 2.9375 (no overflow) 1

Adding Numbers Must align on the decimal point! fpn1.plus(fpn2)? 2.43 + 12.345 ? Must align on the decimal point! fpn1.plus(fpn2)? fpn1.plus(fpn2, resultQ) Must convert fpn1 and fpn2 to resultQ! Do not change either one! Use local variables!

Multiplying Numbers (not in Prog2) 2.44 * 1.2 488 244 2928 2.928 fpn1.times(fpn2, resultQ) intval: fpn1.intVal * fpn2.intVal qVal: fpn1.qVal + fpn2.qVal Must change qVal of the product to resultQ!

Method equals 1 1 Convert fpn1 to qVal 2 intVal = 37 fpn1: intVal = 149 qVal = 4 fpn1: intVal = 37 qVal = 2 1 1 Convert fpn1 to qVal 2 intVal = 37 Convert fpn2 to qVal 4 intVal = 148 1 1 Fpn1.equals(fpn2): false

Method equals 1 1 Convert fpn1 to qVal 2 intVal = 37 fpn1: intVal = 148 qVal = 4 fpn1: intVal = 37 qVal = 2 1 1 Convert fpn1 to qVal 2 intVal = 37 Convert fpn2 to qVal 4 intVal = 148 1 1 Fpn1.equals(fpn2): true

Method lessThan Convert to the smaller qVal Compare intVal after conversion When returns true, it is smaller When returns false, still could be smaller

Schedule Quiz 3: Next Monday Lab 4: Due next Wednesday Lab 5: Due following Monday Lab 6: following Wednesday Prog2: following Friday Lab4, Lab5 and Lab6 are part of Prog2

Lab 3 Put your entire UserName_Lab3 project folder under your individual folder on K:\ drive