[CrashCourse CS] #4 Representing Numbers and Letters with Binary

How to represent things beyond just two values (true, false)?

Decimal

• 263 represents:

100's	10's	1's
2	6	3

• Add these together to make 263.
• Each multiplier is 10 times larger than the one to the right, b/c each column has 10 possible digits to work with, 0 through 9, after which you carry on to the next column.
• Base ten notation, decimal.

Binary

• Binary number 101:

4's	2's	1's
1	0	1

• Add these together to make 5.
• Each multiplier is 2 times larger than the one to the right, b/c each column has 2 possible digits to work with, 0 through 2, after which you carry on to the next column.
• It means that each multiplier has to be two times larger than the column to its right.

Bit

• Each of these binary digits, 1 or 0, is called "bit".
• ex) 1011 1111 -> 8 bit number, with lowest value of 0 (0000 0000), highest value of 255 (1111 1111).
  • 256 different values, or 2^8.
• 8 bit computers, 8bit graphics, audio -> do most of their operations in chunks of 8bits.
  • 256 colors
• 8 bit = 1 byte.
• 32 bit / 64 bit computers - they operate in chunks of 32 or 64 bits.
  • Largest number you can represent with 32 bits is under 4.3 billion.
  • Computers use 32 bit color graphics - makes photo smooth.

How to represent positive/negative numbers

• Most computers use first bit for the sign.
  • 0 for +, 1 for -
  • Use the remaining 31 bits for the number itself.
• 32 bit can represent +/- 2 billion numbers.
• 64 bit can represent +/- 9.2 quintillion numbers.

Numbers that are not whole numbers(정수): 2.415, ...

• They are called "Floating Point Numbers", because the decimal point can float around in the middle of a number.
• The most common method to represent floating point numbers is IEEE754.
  • 625.9 = 0.6259 x 10^3
  • 0.6259 : significand
  • 10^3 : exponent
• In 32-bit floating point number:
  • 1st bit : represents +/-
  • next 8 bits : store exponent (10^3)
  • remaining 23 bits : store significand (.6259)

Computer uses numbers to represnet letters.

• ASCII : the American Standard Code for Information Interchange
  • 7-bit code, stores 128 different values

• ASCII becomes the standard, allowing different computers built by different companies to exchange data : Inter-operability(상호운용성)
• Each country invented multi-byte encoding schemes, all of which were mutually incompatible.
• UNICODE was devised in 1992 for one universal encoding scheme.

Other file formats like MP3 or GIF use binary numbers to encode sounds or colors of a pixel.
Everything on computer is a long sequence of 1's and 0's.

Thoughts

• Float 타입이 소수점이 float 할 수 있어서 그런 이름이 붙여진게 흥미로웠다.