1. EPSII
59:006
Spring 2004

2. Numbers in Computers Why use data types?
Number systems - binary, octal, decimal, hexadecimal
Data representation - bits, bytes, words (of different sizes)
Types
Integer
Char
Float, Double
Signed, Unsigned

3. Data Types Variables are names for places in memory
There are different types of variables
Different variables require different amounts of information to store them
In C the main types are:
char, int, float, double

4. How the Computer Stores Variables
Computers must code each variable into series of electronic “on” and “off” switches.
Information (both instructions and data) are represented by binary codes (1’s and O’s).

5. Binary Numbers 1111 == 15 1000 0000 == 128 1111 1111 == 255 0 == 0
10 == 2
11 == 3
100 == 4
101== 5
110 == 6
111 == 7
1000 == 8
1111 == 15
== 128
== 255

6. Breaking It Down! Binary: a3*23 + a2*22 + a1*21 + a0*20
1001 = 1*23 + 0*22 + 0*21 + 1*20
1001 = 1*8 + 0*4 + 0*2 + 1*1
1001 = 8+1
1001 = 9
Decimal:
a3 a2 a1 a0 = a3 * a2*102 + a1*101 + a0*100

7. Question
What does
Equal in decimal?

8. Solution =
= 29

9. Hexadecimal
Binary is a pain to work with because the representation is so long
There are 16 possible combination of 4 binary digits

10. Hexadecimal Code 0000 == 0 == 0 0001 == 1 == 1 0010 == 2 == 2
0011 == 3 == 3
0100 == 4 == 4
0101 == 5 == 5
0110 == 6 == 6
0111 == 7 == 7
1000 == 8 == 8
1001 == 9 == 9
1010 == 10 == A
1011 == 11 == B
1100 == 12 == C
1101 == 13 == D
1110 == 14 == E
1111 == 15 == F

11. Question
What is the octal code?

12. Answer
a3a2a1a0 Octal =
a3*83 + a2*82 + a1*81 + a0*80

13. Exercise
Convert A9 to binary
Convert to Hex

14. Solution
Convert A9 to binary
Convert to Hex
D C

15. How Do All These Bits Get Organized?
byte n. - A sequence of adjacent bits, usually eight, operated on as a unit by a computer.
word n. - Computer Science. A set of bits constituting the primary unit of addressable memory.
4 bits = nibble = 16 states (24)
8 bits = byte = 256 states (28)
16 bits = word = states (216) => 64K
Memory is arranged in bytes – each individual address points to the beginning of a byte.

16. How are variables stored?
Characters are stored as numbers:
ASCII : ftp://dkuug.dk/i18n/WG15-collection/charmaps/ANSI_X
Unicode over characters – every written language.
Integers stored as binary
Floating point numbers are stored with limited precision according to the IEEE standard.
Double precision floats (type double) are preferred for numerical calculations.

17. Standard Variable Type Storage
Used For
Storage (bytes)
int
Integers
4 (usually, but is really
implementation-dependent)
char
Characters 1
float
Real numbers 4
double 8

18. Other Variable Types Type unsigned positive Integers
4 (usually, but is really
implementation-dependent)
short
integers 2
long
4 (usually)

19. Variable Type Storage Type Storage (bytes) Range of Values int 4
char 1
-128 to 127
float
e-38 to e+38
double 8
e-308 to e+308

20. Finding variable sizes for your computer
Use the sizeof() function:
printf(“An int is %d bytes ”,sizeof(int));
printf(“and a char is %d bytes\n”,sizeof(char));