1. FUNDAMENTAL DATA TYPES CSC 171 LECTURE 4

2. How do Computers represent information? Computers are switches Switches are “on” or “off” Suppose we want to represent something We can decide to interpret (semantics) an “on” switch as a “1” and an “off” switch as a “0”

3. How many possibilities? 1 switch 2 switches 3 switches … “n” switches

4. A “code” Ceasar Cipher – Shift the letters TED becomes VGF Something is represented as something else AC BD CE DF EG FH ……

5. Coding Letters How many letters? How many “switches” (bits)

6. What is a number? 324 A number is a shorthand for a polynomial 324 “means” (3*100)+(2*10)+(4*1) Or : (3*10 2 )+(2*10 1 )+(4*10 0 ) Why do we use 10 numerals? {0,1,2,3,4,5,6,7,8,9}

7. A possible code Every letter is a 26 bit sequence A is “10000000000000000000000000” B is “01000000000000000000000000” “TED” is : – 00000000000000000010000000 00001000000000000000000000 00010000000000000000000000

8. A beter code Use all possible combinations TED becomes 010110010000011 A00000 B00001 C00010 D00011 E00100 F00101 ……

9. What is a number? 324 A number is a shorthand for a polynomial 324 “means” (3*100)+(2*10)+(4*1) Or : (3*10 2 )+(2*10 1 )+(4*10 0 ) Why do we use 10 numerals? {0,1,2,3,4,5,6,7,8,9}

10. Binary Digits (bits) Since computers only have two states they count in base 2 (binary) 1101 2 1101 2 = (1*8)+(1*4)+(0*2)+(1*1) Or = (1*2 3 )+(1*2 2 )+(0*2 1 )+(1*2 0 ) Or = 13 10 Note: 8 “bits” is a “byte”

11. PAIRS EXCERCISE Convert the following binary numbers into base 10 10101 00111 11010 01010 abcde = (a*2 4 )+(b*2 3 )+(c*2 2 )+(d*2 1 )+(e*2 0 )

12. And, of course Convert the following base 10 numbers into binary 7, 12, 5, 19 abcde=(a*2 4 )+(b*2 3 )+(c*2 2 )+(d*2 1 )+(e*2 0 )

13. NUMBER TYPES IN JAVA int : integers, no fractional part – 1 – -4 – 0 double: floating point numbers – 0.5 – 0.0 – -3.1111

14. Operations depend on type “/” is the division operator 7.0 / 4.0 yields 1.75 7 / 4 yields 1 Note the “remainder” operator is useful for integers 7 % 4 yields 3

15. “PRIMITIVE” types in JAVA boolean8 bits char16 bits byte8 bits short16 bits int32 bits long64 bits float32 bits double64 bits

16. Assignment public void addNickels(int count) { nickels = nickels + count; }

17. Need to draw this

18. Increment and decrement nickles++ is shorthand for nickles = nickles + 1; or Nickles += 1;

19. Some shorthand options int count; count = 0; count++; count--; ++count; --count;

20. Constant variables Sort of like “jumbo shrimp” or “freezer burn”? “Magic numbers” are bad style (to the blackboard, robin!)

21. Static finals Enable constants Math.PI Enable functions Math.sqrt(x)