Binary and Hard Disk PEOPLE Program Good afternoon everyone, welcome to the Binary section of PEOPLE program. 2 day event, today talk,

How do Computers Store Numbers Computers are constructed of digital electronics => two states: “on” “off” Binary number system consists of 0 and 1 only On-off patterns are used to encode numbers using binary number system Most computer electronics Voltage levels CD-ROM Microscopic dark spots on disk surface Hard disk Magnetism Computer memory Electric charges on capacitors As you may have learnt before Two states which can represent 0 and 1 resepectively

Binary numbers are great! Simple to work with No big addition and multiplication tables to learn Just do same things over and over very fast Just use two values of voltage, magnetism or other signal Hardware easier to design and more resistant For example, for decimal system, 45 rules; for binary, 4 rules Better robustness

Hard Drive Hard disks are used in all desktop computers, servers, super computers etc. They are also VCR type devices or video recorders that use hard drives instead of tape They store changing digital information in a relatively permanent form. They give computers the ability to remember things when the power goes out. Different from RAM, where info will be lost after turn off power.

How Does Binary Work? Decimal number system Expanded notation: … 1000 10 digits (0 to 9) Add a second column worth 10 times the value of the first column Expanded notation: 3 x 100 + 6 x 10 + 5 = 365 1 x 1000 + 0 x 100 + 3 x 10 + 2 = 1032 … 1000 100 10 1 Or 10 to the first, or 10 to the second

Binary Number System Only contains two digits: 0,1 Add a second column worth 2 times the value of the first column To convert a number from binary to decimal, use expanded notation: 101101 = 1x32 + 0x16 + 1x8 + 1x4 + 0x2 + 1x1 = 45   1 … 32 16 8 4 2 1

Binary  Decimal Any desired amount can be represented using 1 and 0. Examples 1 == 0001 3 == 0011 6 == 0110 1  a power of 2 0  zero Examples 0001  2^0 = 1 0010  2^1 = 2 0100  2^2 = 4 1000  2^3 = 8 0101 = 0 + 4 + 0 + 1 = 5 1010 = 8 + 0 + 2 + 0 = 10 0111 = 0 + 4 + 2 + 1 = 7

Larger Numbers Numbers from 1 to 15 0000 = 0 0100 = 4 1000 = 8 1100 = 12 0001 = 1 0101 = 5 1001 = 9 1101 = 13 0010 = 2 0110 = 6 1010 = 10 1110 = 14 0011 = 3 0111 = 7 1011 = 11 1111 = 15 Bigger whole numbers  more bits more places in binary number 10000101 = 128 + 0 + 0 + 0 + 0 + 4 + 0 + 1 = 133 This is 8 bits == 1 byte

Larger Numbers 10000101 = 128 + 0 + 0 + 0 + 0 + 4 + 1 = 133 This is 8 bits == 1 byte Kilobyte = 1024 bytes (1024 = 2^10) Megabyte = 1024 kilobytes ~ a million bytes Gigabyte = 1024 megabytes

Typical Sizes Typical Hard disks are 100 – 500 gigabyte 1 byte == 1 character  hard disk might hold 100 billion characters ~ 20 billion words of raw text Real numbers, fractions, very large numbers  floating point arithmetic

Binary Addition Decimal System Binary System Sum >= 10  add 1 to the column on the left Binary System Sum >= 2  add 1 to the column on the left Example: 1+1+1 = 11 1+1+1+1 = 100 110101 + 11110 -------------- 1010011

Binary Addition Second Way Convert the numbers to decimal Add the decimal numbers Convert the sum to binary

ASCII Table ASCII: American Standard Code for Information Interchange Alphanumeric characters are represented with 8 bits A  65 == 01000001 Write 3 letters in ASCII Table How to represent letters in computers? Pass ASCII Table to students