# CS 202 - Notes 2018-09-21

# It's all about the bits

All information in the computer are stored as as patterns of bits.

Given N bits, we can make 2^N different patterns. These could be numbers, letters, or anything else we want to represent.

basic sizes:bit, byte (8 bits)

Prefix (base 10)	Meaning (base 10)	Abbrv (base 10)	Prefix (base 2)	Meaning (base 2)	Abbrv (base 2)
kilo-	103	KB	210	kibi-	KiB
mega-	106	MB	220	mebi-	MiB
giga-	109	GB	230	gibi-	GiB
tera-	1012	TB	240	tebi-	TiB
peta-	1015	PB	250	pebi-	PiB
exa-	1018	EB	260	exbi-	EiB
zetta-	1021	ZB	270	zebi-	ZiB
yotta-	1024	YB	280	yobi-	YiB

All of the abbreviations are in bytes. If we want to talk about bits, we use a lowercase b (Kb, Mb, etc...)

The base two prefixes have not fully caught on. This is problematic because there is an increasing discrepancy between the base 10 and base 2 meanings.

1000 vs 1024 (K vs Ki) is not a huge difference 1000000000 vs 1073741824 (G vs. Gi) starts being a bit significant

Another unit of size is the word. In theory, this is the native unit of size for the computer, but for reasons of compatibility, on our machines, this has been frozen at 16 bits for some time.

# Numbers and Bases

To make it easier to deal with bit patterns, we treat them as if they were binary numbers.

Decimal values are convenient, but it isn't easy to do conversions because 10 is not a power of two. So, we frequently will make use of other bases that are more compact than binary, but still powers of two.

# Octal (base 8)

In base 8, each digit can be one of eight values (0,1,2,3,4,5,6,7).

Conversion is simple, because we exhaust all combinations of three bits in eight combinations as well. So, we can convert from binary to octal by breaking the pattern into blocks of three and converting each block separately. Conversely, converting from octal to binary just means converting each digit of octal to the corresponding three bits of binary.

Decimal	Binary	Octal
0	0000	0
1	0001	1
2	0010	2
3	0011	3
4	0100	4
5	0101	5
6	0110	6
7	0111	7
8	1000	10
9	1001	11
10	1010	12

Example: 1 011 011 101₂ = 1335₈

Example: 726₈ = 111 010 110₂

# Hexadecimal (base 16)

Base 16 is more common because it is more compact. Each digit can be one of 16 values (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F).

Decimal	Binary	Hex
0	00000	0
1	00001	1
2	00010	2
3	00011	3
4	00100	4
5	00101	5
6	00110	6
7	00111	7
8	01000	8
9	01001	9
10	01010	A
11	01011	B
12	01100	C
13	01101	D
14	01110	E
15	01111	F
16	10000	10
17	10001	11

Example: 10 1011 0110₂ = 2B6₁₆

Example: 5AF₁₆ = 0101 1010 1111₂