1. Bit-Level Discussion of Numeric Types
Homework 2 has been extended to October 4th, 2017
Finish reading Chapter 2 of Kernigan and Ritchie

2. Review of char and int types
char type
8 bits, 1 byte
Example:
int type
32 bits, 4 bytes
'\x5d' 93
']'
0x6ace9718

3. Numeric Literals signed char literals signed int literals Example:
Will be treated as an r-value of type signed char
signed int literals
Will be treated as an r-value of type signed int
'\x##'
0x########

4. Explicit Casting
Casting is the act of converting an r-value from one type to another.
In most cases, this results in a change in bit-length of the value.
Example: In memory:
Another example: Note, large  small drops bits
char c = '\x55';
int i = (int) c;
int i = 0x7fff9876;
char c = (char) i;

5. Implicit Casting
Just like Explicit Casting, but doesn't use the (type) operator.
Example:
The value of variable c must be converted to type (int) before arithmetic can be done between it and the value of variable i.
char c = 100;
int i = 100;
printf("%d\n", c * i);

6. Negative Numbers
To describe negative numbers, we need to make use of a property of binary arithmetic.
Let's do this by first defining our first negative number: -1
Negative one (-1) is the number to which adding one (+1) will give us zero (0) There is only one such number: Note, adding +1 to that number actually gives us but we can't retain the carry.
XXXX XXXX

7. One's Complement
So, to define negative numbers in general, we need a few steps.
First, we'll define the One's Complement operator (~):
For any number, take it's binary representation and flip/toggle each bit.
Examples: ~ ~
~0x
0xbeefface
~0x
0xcafebabe

8. Two's Complement
Using the One's Complement (~) we can define the Two's Complement as something we're familiar with: The Negative operator (–)
The Two's Complement is equivalent to the One's Complement Plus One.
Example: ~
= -87
= 87
~ a9 56 56
+ 01 57
\xa9 = -87
\x57 = 87

9. Fast One's Complement in Hex
Due to the fact that hex digits are just groups of four binary digits, we can perform One's Complement on them as a grouping.
To perform One's Complement this way, switch hex digits (groups of 4 bits) horizontally. f 1 e 2 d 3 c 4 b 5 a 6 9 7 8
0000
1111
0001
1110
0010
1101
0011
1100
0100
1011
0101
1010
0110
1001
0111
1000

10. Casting Revisited (with Negative Numbers)
Now that we know how to represent negative numbers, there's an important behavior to describe in casting.
The left-most bit of a numeric type is the Most Significant Bit (MSB)
This bit corresponds to the sign of a number (positive or negative, +/–)
When casting from a smaller signed type to a larger signed type, the sign expands across all added bits.
Example: (int) 1 1
Note: This still corresponds to the same negative number!