0 1 2 3 4 5 6 7 8 9
When we add, say, 26 to 18, we do:
1
26
+ 18
--
64
0, 1, 10, 11, 100, 101, 110, 111and so forth. Arithmetic is base 2 instead of 10, e.g.
1
111 7
+ 010 2
--- =
1001 9
Computers store information as numbers, and numbers in this binary system.
Each binary digit is called a bit, i.e., the capacity to store one or zero.
How many numbers can we represent with a one-bit number? Two: 0 and 1.
With a two-bit number? Four: 00 01 10 11
With a three-bit number? Eight:
000 001 010 011 100 101 110 111With an n-bit number? Two the the n power.
Negative numbers are represented using a system called two's complement. We won't go into that, but it basically means that one bit is designated as the "sign bit," recording whether or not the number is negative.
Often bytes grouped into four to represent large integers. How many bits in four bytes? 32. So there are 2 to the 32nd = 4294967296 different bit combinations. That gives us the integers from -2147483648 to 2147483647, including 0.
We can also use bits to represent logic. Zero means FALSE and One means TRUE. More about this later...
Binary Decimal Hexadecimal Binary Decimal Hexadecimal 0000 0 0 1000 8 8 0001 1 1 1001 9 9 0010 2 2 1010 10 A 0011 3 3 1011 11 B 0100 4 4 1100 12 C 0101 5 5 1101 13 D 0110 6 6 1110 14 E 0111 7 7 1111 15 FConverting from binary to hexadecimal and back is easy. For instance, 100 binary is 64 hexadecimal. To convert to binary, we just substitute the binary equivalent for 6 and 4, e.g. 01100100. So 100 decimal is 01100100 binary. Knowing about hexadecimal and binary become more important as you explore the inner workings of the computer.
This table shows the ASCII, giving the numeric code as well as the character represented:
Dec Hex Char Dec Hex Char
------------------------------------------------
0 00 NUL '\0' 64 40 @
1 01 SOH 65 41 A
2 02 STX 66 42 B
3 03 ETX 67 43 C
4 04 EOT 68 44 D
5 05 ENQ 69 45 E
6 06 ACK 70 46 F
7 07 BEL '\a' 71 47 G
8 08 BS '\b' 72 48 H
9 09 HT '\t' 73 49 I
10 0A LF '\n' 74 4A J
11 0B VT '\v' 75 4B K
12 0C FF '\f' 76 4C L
13 0D CR '\r' 77 4D M
14 0E SO 78 4E N
15 0F SI 79 4F O
16 10 DLE 80 50 P
17 11 DC1 81 51 Q
18 12 DC2 82 52 R
19 13 DC3 83 53 S
20 14 DC4 84 54 T
21 15 NAK 85 55 U
22 16 SYN 86 56 V
23 17 ETB 87 57 W
24 18 CAN 88 58 X
25 19 EM 89 59 Y
26 1A SUB 90 5A Z
27 1B ESC 91 5B [
28 1C FS 92 5C \ '\\'
29 1D GS 93 5D ]
30 1E RS 94 5E ^
31 1F US 95 5F _
32 20 SPACE 96 60 `
33 21 ! 97 61 a
34 22 " 98 62 b
35 23 # 99 63 c
+ solid state physics - explains the way a transistor functions.
+ lowest level hardware - bare metal, ensembles of transistors.
+ low level hardware - logic gates, sequential logic, bits and bytes, chips.
+ mid level hardware - components, motherboards, disk drives, RAM chips, etc.
/ \
/ \
/ \
/ \
software high level hardware
+ machine language - interface peripherals: printer, keyboard,
to hardware, CPU instructions, mouse, etc.
registers, i/o ports, dma,
network interface hardware, interrupt handlers, kernel/user mode.
+ assembly language - low-level language, "assembled" into machine language.
some parts of the operating system written in assembly. many device
drivers have assembly content.
+ operating system kernel, done in mostly C and assembler
at a "low" level. code is written for the sake of the computer; user
usually doesn't need to use it directly. example: fetching a particular
block from the hard disk where the file system knows a piece of data lives.
+ systems programming. more computing for the sake of the computer, but more
accessible to the user. 'ls' is an example. windowing systems another
example. compilers another example. mostly done in C, sometimes assembler.
+ applications programming - most of apps written in HLL such as C/C++,
Pascal, FORTRAN, Java, Lisp, Prolog, etc.
+ user-level apps, word processors, web browsers, spreadsheets, etc.