MAT 152 - SAS # 2 - 6

• Binary Code


  is a coding system that utilizes a letter, a digit, and or character in an electronic device such as computers.
• Binary Code


  It is presented by binary "bits" 1 and 0 which are used as a group of binary digits and are used for processing computer instructions and data, picture, and text, etc.
• The circuits in a computer's processir are made up of billions and transistors.
• Transistor


  is a tiny switch activated by the electronic signals it receives.
• 1


  on
• 0


  off
• Computer programs


  are sets of instructions. Each instruction is translated into machine code - simple binary codes that activate the CPU. Programmers write computer code and this is converted by a translator into binary instructions that the processor can execute. All software, music, documents, and any other information that is processed by a computer, is also stored using binary.
• Encoding


  Everything on a computer is represented as streams of binary numbers. Audio, images, and characters all look like binary numbers in a machine code.
• Audio encoding formats


  mp3, WAV, AAC
• Video encoding formats


  MPEG4, H264
• Text encoding formats


  ASCII, Unicode
• Images encoding formats


  BMP, JPEG, PNG
• Byte


  8 bits
• Nibble


  half-byte, 4 bits
• Kilobyte (KB)


  1,000 bytes
• Megabyte (MB)


  1,000 kilobytes
• Gigabyte (GB)


  1,000 megabytes
• Terabyte (TB)


  1,000 gigabytes
• Base 2/Binary System


  composed of two values: 0 and 1.
• Base 8/Octal System


  eight values: 0, 1, 2, 3, 4, 5, 6, 7
• Base 10/Decimal System


  composed of ten values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• Base 16/Hexadecimal System


  Composed of 16 values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
• In a number system, each number is represented by its base.
• Binary addition is similar to decimal number system. But the main difference is, binary number system uses two digits like 0 and 1.
• Binary addition 


  is performed similar to the common addition. However, values carried over are different.
• Basic rules of binary addition

  0 + 0 = 0

  0 + 1 = 1

  1 + 0 = 1

  1 + 1 = 10
• Modular Arithmetic


  is a system of arithmetic for integers, where the numbers wrap around upon reaching a certain value, the modulus (plural moduli). It is also known for taking the remainder.
• Modular arithmetic


  a - b/n; n = modulus
• In addition, if n > 0 and r is the remainder when the Division Algorithm is used to divide b by n, then r i called the least residue.
• A set of integers is called complete residue system modulo n, if it contains exactly one integer from each equivalence class modulo n.
• In modular arithmetic, arithmetic operations are performed then the answer is divided by the modulus.
• The result of an arithmetic operation mod n is always a whole number less than n.