1. COMPUTER 2430 Object Oriented Programming and Data Structures I

2. Fixed Point Numbers Prog3
Computers need to perform floating point calculations
Microprocessor chosen doesn't have a floating point capability

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

4. How to Store Integers in Computer
Binary Number 1
Decimal Number: 143

5. How to Store Signed Integers
Binary Number
Sign bit 1
Decimal Number: -15

6. How to Store Signed Integers
Binary Number
Sign bit 1
Decimal Number: +15

7. Prog3 Integers are 4 bytes, 32 bits
We only consider positive numbers and ignore the sign: 31 bits only

8. How to Store Positive Double Numbers
Implicit binary point
qVal: 2
Fixed Point Number:
intVal
qVal

9. How to Store Positive Double Numbers
Implicit Binary Point : qVal = 2 1
Decimal Number:

10. How to Store Positive Double Numbers
Implicit Binary Point : qVal = 2
Decimal Number:
* 22 =
= 143 1
143.0 / 22 =

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

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

13. How to Store Positive Double Numbers
Fixed Point Number: qVal = 4 1
Decimal Number:

14. How to Store Positive Double Numbers
Fixed Point Number: qVal = 4
Decimal Number:
* 24 =
= 143 1
143.0 / 24 =

15. How to Store Data in Computer1
Char: ?
Integer
143
Fixed Point Number: qVal = 4
8.9375
Fixed Point Number: qVal = 2
37.75

16. Shift Operator 1
x: 40
x >> 2
New value: 10 (40 / 22 ) 1

17. Shift Operator 1
x: 40
x << 2
New value: 160 (40 * 22 ) 1

18. Shift Operator 1
x: 40
x >> 4
New value: 2 (Underflow) 1

19. Shift Operator 1
x: 40
x << 4
New value: 128 (Overflow) 1

20. Prog3
We ignore overflows
Underflows are not totally ignored

21. Shift Operator 1 x: 40 x >> -2 New value: 0 x << -21
x: 40
x >> -2
New value: 0
x << -2
Don’t do it!
Use IF statement!

22. Change qVal 1 dbl: 8.9375 Fixed Point Number: dbl * 24
dbl:
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

23. Change qVal 1 dbl: 2.9375 Fixed Point Number: dbl * 241
dbl:
Fixed Point Number: dbl * 24
qVal: 4, intVal: 47
Change qVal to 6: dbl * 26
intVal = intVal << 2
(no overflow) 1

24. Adding Numbers Must align on the decimal point! fpn1.plus(fpn2)?
2.43 ?
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!

25. Multiplying Numbers (not in Prog3)
2.44 *
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!

26. Method equals 1 1 Convert fpn1 to qVal 2 intVal = 37
fpn1: intVal = 149
qVal = 4
fpn2: 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

27. Method equals 1 1 Convert fpn1 to qVal 2 intVal = 37
fpn1: intVal = 148
qVal = 4
fpn2: 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

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

29. Test 1
Wednesday, October 10
Note01 – Note14
No FixedPoint

30. Schedule Lab 4: Due Monday, October 15
Lab 5: Due Wednesday, October 17
Prog3: Due Wednesday, October 24
Lab4 and Lab5 are part of Prog3

31. Prog2
Grace Time
10 PM, October 8