1. LING 388: Computers and Language
Lecture 3

2. Today's Topics Review Quick Homework 2 Quick Homework 3
Underneath Python
Binary
Numbers
Character sets

3. Homework 2 review: Egghead
1952

4. Homework 2 review: Egghead
nerd or geek
"While its true origins are a bit murky, it's widely agreed that "egghead" reached the height of its usage in 1952, when then-vice-presidential candidate Richard Nixon used it to describe the Democratic candidate for president, Adlai Stevenson -- whose balding head certainly conjured images of an egg. But his supporters were quickly labeled eggheads as well, and thus the term took on a political meaning. It came, eventually, to mean approximately what the word "elitist" means today."
Adlai Stevenson
(source: Wikipedia)

5. Python: Numbers
import math
math.pi

6. Python: Numbers Identities: one here one for your homework
Two decimal places:
'{:.2f}'.format(i)
Let's define a function for this identity

7. Quick Homework 3 Complex number library: i is j in Python:
cmath
g/3.0/library/cmath.ht ml
i is j in Python:
>>> cmath.sqrt(-1) 1j
Demonstrate Euler's identity in Python
Due date Monday (midnight)

8. The underlying architecture
Python is a high-level language
Beneath Python lies binary…
interesting use of binary notation:
6 bit Leica camera lens encoding
The 6-bit code shown on the right
is (1 = black, 0 = white), 
read starting from the philips
screw head

9. Introduction Memory Representation binary: zeros and ones (1 bit)
array
a[23]
addressable
Memory
(RAM)
Memory Representation
binary: zeros and ones (1 bit)
organized into bytes (8 bits)
memory is byte-addressable
word (32 bits)
e.g. integer
(64 bits: floating point number)
big-endian/little-endian
most significant byte first or least significant byte
communication …
your Intel and ARM CPUs
FFFFFFFF

10. Increased address space and 64-bit registers
Introduction
Increased address space and 64-bit registers
A typical notebook computer
Example: a 2013 Macbook Air
CPU: Core i5-4250U
1.3 billion transistors
built-in GPU
TDP: 15W (1.3 GHz)
Dual core (Turbo: 2.6 GHz)
Hyper-Threaded (4 logical CPUs, 2 physical)
64 bit
64 KB (32 KB Instruction + 32 KB Data) L1 cache
256 KB L2 cache per core
12MB L3 cache shared
16GB max RAM
A 4 core machine: 8 virtual
anandtech.com

11. Introduction Machine Language
A CPU understands only one language: machine language
all other languages must be translated into machine language
Primitive instructions include:
MOV
PUSH
POP
ADD / SUB
INC / DEC
IMUL / IDIV
AND / OR / XOR / NOT
NEG
SHL / SHR
JMP
CMP
JE / JNE / JZ / JG / JGE / JL / JLE
CALL / RET
Assembly Language: (this notation)
by definition, nothing built on it is more powerful

12. Introduction
Not all the machine instructions are conceptually necessary
many provided for speed/efficiency
Theoretical Computer Science
All mechanical computation can be carried out using a TURING MACHINE
Finite state table + (infinite) tape
Tape instructions:
at the tape head: Erase, Write, Move (Left/Right/NoMove)
Finite state table:
Current state x Tape symbol --> new state x New Tape symbol x Move

13. Introduction Storage: based on digital logic
binary (base 2) – everything is a power of 2
Byte: 8 bits = =
= 91 (in decimal)
Hexadecimal (base 16)
0-9,A,B,C,D,E,F (need 4 bits)
5B (= 1 byte)
= 5* =
= 91 27 26 25 24 23 22 21 20 1 27 26 25 24 23 22 21 20 23 22 21 20 1 23 22 21 20 23 22 21 20 1 5 B
161
160 5 B
161
160

14. Introduction: data types
Integers
In one byte (= 8 bits), what’s the largest and smallest number, we can represent?
Answer:
Why? – 1
= 0
= 127
= -128
= -1 27 26 25 24 23 22 21 20 1 27 26 25 24 23 22 21 20 27 26 25 24 23 22 21 20
28 – 1 = 255 27 26 25 24 23 22 21 20 1 27 26 25 24 23 22 21 20
27 – 1 = 127 27 26 25 24 23 22 21 20 1

15. Introduction: data types
Integers
In one byte (= 8 bits), what’s the largest and smallest number, we can represent?
= 0
= 127
= -128
= -1 …
127
-128
-127 -1
2’s complement representation

16. Introduction: data types
Integers
In one byte, what’s the largest and smallest number, we can represent?
Answer: using the 2’s complement representation
Why? super-convenient for arithmetic operations
“to convert a positive integer X to its negative counterpart, flip all the bits, and add 1”
Example:
= = 10 (decimal)
= = -10 (decimal)
flip + 1 = =
Addition: =
= 0 (ignore overflow)

17. Introduction: data types
Typically 32 bits (4 bytes) are used to store an integer
range: -2,147,483,648 ( ) to 2,147,483,647 ( )
what if you want to store even larger numbers?
Binary Coded Decimal (BCD)
code each decimal digit separately, use a string (sequence) of decimal digits …
231
230
229
228
227
226
225
224 … 27 26 25 24 23 22 21 20
byte 3
byte 2
byte 1
byte 0 C:
int

18. Introduction: data types
what if you want to store even larger numbers?
Binary Coded Decimal (BCD)
1 byte can code two digits (0-9 requires 4 bits)
1 nibble (4 bits) codes the sign (+/-), e.g. hex C/D 23 22 21 20 2 1 4
2 bytes (= 4 nibbles) 23 22 21 20 1 1 + 2 1 4
2.5 bytes (= 5 nibbles) 23 22 21 20 1 9
credit (+)
debit (-) 23 22 21 20 1 23 22 21 20 1 C D

19. Introduction: data types
Typically, 64 bits (8 bytes) are used to represent floating point numbers (double precision)
c = x 108 (m/s)
coefficient: 52 bits (implied 1, therefore treat as 53)
exponent: 11 bits (not 2’s complement, unsigned with bias)
sign: 1 bit (+/-) C:
float
double
x86 CPUs have a built-in
floating point coprocessor (x87)
80 bit long registers
wikipedia

20. Introduction: data types
char
How about letters, punctuation, etc.?
ASCII
American Standard Code for Information Interchange
Based on English alphabet (upper and lower case) + space + digits + punctuation + control (Teletype Model 33)
Question: how many bits do we need?
7 bits + 1 bit parity
Remember everything is in binary …
Teletype Model 33 ASR
Teleprinter (Wikipedia)

21. Introduction: data types
order is important in sorting!
0-9: there’s a connection with BCD. Notice: code 30 (hex) through 39 (hex)

22. Introduction: data types
x86 assemby language:
PF: even parity flag set by
arithmetic ops.
TEST: AND (don’t store result), sets PF
JP: jump if PF set
Example:
MOV al,<char>
TEST al, al
JP <location if even>
<go here if odd>
Parity bit:
transmission can be noisy
parity bit can be added to ASCII code
can spot single bit transmission errors
even/odd parity:
receiver understands each byte should be even/odd
Example:
0 (zero) is ASCII 30 (hex) =
even parity: , odd parity:
Checking parity:
Exclusive or (XOR): basic machine instruction
A xor B true if either A or B true but not both
(even parity 0) xor bit by bit
0 xor 1 = 1 xor 1 = 0 xor 0 = 0 xor 0 = 0 xor 0 = 0 xor 0 = 0 xor 0 = 0

23. Introduction: data types
UTF-8
standard in the post-ASCII world
backwards compatible with ASCII
(previously, different languages had multi-byte character sets that clashed)
Universal Character Set (UCS) Transformation Format 8-bits
(Wikipedia)

24. Introduction: data types
Example:
あ Hiragana letter A: UTF-8: E38182
Byte 1: E = 1110, 3 = 0011
Byte 2: 8 = 1000, 1 = 0001
Byte 3: 8 = 1000, 2 = 0010
い Hiragana letter I: UTF-8: E38184
Shift-JIS (Hex):
あ: 82A0
い: 82A2

25. Introduction: data types
How can you tell what encoding your file is using?
Detecting UTF-8
Microsoft:
1st three bytes in the file is EF BB BF
(not all software understands this; not everybody uses it)
HTML:
<meta http-equiv="Content-Type" content="text/html;charset=UTF-8" >
(not always present)
Analyze the file:
Find non-valid UTF-8 sequences: if found, not UTF-8…
Interesting paper:

26. Introduction: data types
Text files:
text files have lines: how do we mark the end of a line?
End of line (EOL) control character(s):
LF 0x0A (Mac/Linux),
CR 0x0D (Old Macs),
CR+LF 0x0D0A (Windows)
End of file (EOF) control character:
(EOT) 0x04 (aka Control-D)
programming languages:
NUL used to mark
the end of a string
binaryvision.nl