User:Delimiter/Presentations/Mathematics
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Introduction
This page is a syllabus for my class on Computer Mathematics- "Numbers, Units and Time for Computing"
The audience is Beginner. Give them a basis for interpreting the numbers, numerical units and timestamps seen on a modern-day operating system.
Disclaimer
- I am not a math teacher
- The class is about numbers and units used by computers (thus humans)
- It is not about using computers for math - visualization, analysis, spreadsheets and so on.
- Solid understanding of these concepts will help anyone succeed in working with computers & network administration
About me
Mark Foster is a technical expert with nearly 20 years of system/network administration and programming. More can be found at http://mark.foster.cc
Base number systems
Decimal Numbers
- 0-9 just add more columns for powers of 10
- In other words, Base-10
- 10^1, 10^2
- The meaning of 0 (Zero)
- Computers start counting at 0, not 1
Binary Numbers
- Let's start small
- 0-1
- Base-2
Hexadecimal Numbers
- 0-9,A-F
- Base-16
Octal
- 0-7
- Base-8
Time & Clocks
- Day = 24 hours = 0-23
- Hour = 60 minutes = 0-59
- Minute = 60 seconds = 0-59
- Second = 1000 milliseconds (ms)
- Millisecond = 1000 microseconds (us)
- Microsecond = 1000 nanoseconds (ns)
DD:HH:MM:SS:xxxyyyzzz
Bits, Bytes and Megabytes
Representations of binary number units and lengths
- bit
- nibble
- byte
- octet - different than octal
- word
- Kilo, Mega, Giga, Tera, Peta
- Megapixels (Cameras)
- 720p, 1080p (Televisions)
- Common VGA resolutions (LCD/CRT Monitors)
- Common Video resolutions i.e. miniDV
Putting it together
- Octet vs. Byte (word-size)
- Signed vs. Unsigned
- Bit-shifting
- Shorts, Longs
- Floating point
- Block sizes
- Little-endian vs. Big-endian
- Interesting #s in computers
2^16 - 1 = 65535 <-- Maximum value for a unsigned 16-bit # 2^32 - 1 = 4294967295 <-- Maximum value for a unsigned 32-bit # 2^64 - 1 = 18446744073709551615 <-- Maximum value for a unsigned 64-bit #
Networking
OSI Layers
MAC Addresses
IPv4
IP Address representation = 32 bits or 4 octets (8-bit bytes)
Netmasks (traditional, hex and CIDR)
- Class A, B, C and E
- /8 /16 /24 /32
- /255.255.255.0 (FFFFFFFFFFFF0000)
- What makes these special? 0.0.0.0 255.255.255.255?
- What are routers. Where is my router? Can I ping it?
- Trivia IP to decimal, a neat trick albeit useless.
IPv6
IP Address representation - 128 bits
Time representation
- Timestamps alterative representation of a moment in time, usually the second
- The Epoch aka Unix time Dec 31 1969 is zero, "Now" is the # of seconds since
- Timezones UTC/GMT, PSTPDT=-0800 or -0700 depending on the time of year
- Daylight savings
- Accuracy: Seconds (s, sec), milliseconds (ms, msec), microseconds (us, usec) and nanoseconds (ns, nsec)
- NTP - network time protocol
Cool Tools
- bc
- Calculator app
- Google as calculator, converter
- Worldtimezone.com http://www.worldtimezone.com/ (online)
- ipcalc(1) - IP subnet calculator
- Speedtest http://www.speedtest.net (online)
- BDP calculator - http://www.speedguide.net/bdp.php (online)
- date (1) - print or set the system date and time
- Timestamp converter (online)