Introduction to Introduction to Computer Science (huh???)

1
Introduction to Introduction to Computer Science
(huh???)

• A very introductory crash course
• Will attempt to cover as many 1st year Computer
  Science topics as possible in 3-4 sessions.
• Topics may include
• Number Representation
• Data Types, Data Structures
• Basic Computer Architecture
• Elementary Searching and Sorting Algorithms

2
Text Books

• Far too many to list
• The BII library is a good source
• The Internet is another
• Try the Idiots series also

3
The Binary System(do we need to go through this?)

• To convert binary to base 10
• For any binary number bn-1bn-2b1b0,
• X bn-1?2n-1 bn-2 ?2n-2b1?2b0
• To convert base 10 to binary
• Divide by 2, note remainder
• Keep dividing and noting remainders until
  result0
• Binary value is the whole series of remainders
  read backwards

4
Word Length

• Myth 64-bit computers are 232 times more
  powerful than 32-bit computers
• Word length refers to the size of CPU registers,
  not processing power
• Affects
• Size of largest integer the computer can directly
  handle
• Amount of directly accessible memory
• Eg. a 32-bit PCs largest signed integer is
  214743647 (231-1) and the largest directly
  accessible memory segment is 4GB.

5
2s Complement

• How to represent negative numbers?
• Consider WLOG an 8-bit word
• If the MSB is 0, ve number
• If MSB is 1, the value is
• - ((b7b6b5b4b3b2b1b0 XOR 11111111) 1)
• E.g.
• 00101101 45
• 11010011 -45

6
Binary Arithmetic
4562107 4562107 4562107 4995144 4995144 4995144 80-7380 -73 7 80-7380 -73 7
00101101 00101101 00101101 00110001 00110001 00110001 01010000 01010000
00111110 00111110 01011111 01011111 01011111 01011111 10110111 10110111 10110111
01101011 10010000 -112? -112? 100000111
(overflow) (overflow) (overflow) (overflow)
43-5643 -56 -13 43-5643 -56 -13 43-5643 -56 -13 -65-96-161 -65-96-161 -65-96-161
00101011 00101011 10111111 10111111 10111111
11001000 11001000 11001000 10100000 10100000 10100000 10100000
11110011 101011111 101011111 95? 95?
(underflow) (underflow) (underflow) (underflow)
Carry in
Carry out

• For correct results either (both carry in and
  carry out) or (no carries)

7
Multiplication and Division

• Multiplication
• Long multiplication possible
• Faster algorithms exist
• Refer to the book by Hennesey and Patterson for
  details
• Division
• So complicated that some systems implement as
  software routine
• Hennesey and Patterson for details

8
Floating Point Numbers

• IEEE 754 the de-facto standard today
• Single Precision

31
30
0
22
23
Significand
Exponent
Assumed decimal point
Sign bit

• Double Precision

63
62
0
51
52
Significand
Exponent
9
IEEE 754

• Normally
• Sign bit is 0 for ve and 1 for ve
• Significand is assumed to be 1.xxxxxx
• Exponent is read as 2k-7 (SP) or 2k-10 (DP)
• Read the number as ?1.Significand ? 2Exponent 7
  (SP) or 10 (DP)
• Otherwise, exceptions as per the table below

Type Sign Exponent Assumed bit Significand
NaN ? 111111 1 1xxx...xxx
SNaN ? 111111 1 0xxxxxx
Infinity ? 111111 1 0
Denormalised ? 0 0 xxxxxx
Zero ? 0 0 0
10
Floating Point Arithmetic

• Addition/Subtraction
• Denormalise smaller number if necessary so that
  both exponents are the same
• Add/subtract significands
• Normalise if necessary
• Multiplication/Division
• Multiply/divide significands
• Add/subtract exponents
• Normalise if necessary