DISCRETE MATH (CONVERSIONS ONLY PANI)

• What is Discrete Mathematics ?


  Discrete mathematics is the study of mathematical structures that are discrete rather than continous. It deals with values can only assume only distinct, separate values.
• Define Discrete Objects


  they are distintinct individual, unique, and are separable
• Examples of discrete objects


  counting numbers, finite sets, as long as they aren't connected and have gaps betweent them.
• Applications of discrete math in Computer science

  Algorithms, data structures, cryptography
• Applications of discrete math in Logic and set theory

  Foundational concepts in reasoning and proofs.
• Application of Discrete mathematics in cobinatorics

  Counting and arrangements
• Applications of discrete mathematics in graph theory

  Networks, paths, and circuits
• What are the key concepts of discerete mathematics?

  Sets, Functions, Relations, Algorithms
• What and when is succesive division used?

  it is a method used to convert numbers from one base to another

  Decimal to all other bases.
• Enumerate the process of succesive division:

  1. Divide the number by new base.
  2. Record the remainder
  3. Repeat with the quotient until the quotient is zero
  4. read the reminders from the most significant bit to the least significant bit (down to up).
• Number Systems is a?


  writing system for expressing numbers, a mathematical notatiotn for representing then numbers of a given set, using digitsor symbols in a consistent manner.
• Radix (Base of a number system)

  determines the how many digits are avalable and the value each digits holds based on the position.
• Key concepts of Number systems

  Base (radix), Positional notation, common number systems
• What is positional notation?

  The value of a digit in a number is determine by its position in the sequence. Each position represents a power of the base.
• Common number systems

  Decimal

  Binary

  octal

  Hexadecimal
• Decimal

  digits 0-9

  commonly used in everyday counting and arithmetic,
• Binary 


  digits 0 and 1 only

  commonly used in computers and digital systems.
• octal 


  digits 0-7

  commonly used in digital systems, shorthand for binary
• Hexadecimal


  0-9 and 10-15 (ABCDEF)

  Used in memory adressing, color codes and web design.
• Decimal to BINARY: SOLVE ALL

  1. 1532
  2. 2784
  3. 4896
  4. 55555
  5. 99999

  ANSWERS:

  1. 10111111100
  2. 101011100000
  3. 1001100100000
  4. 1101100100000011
  5. 11000011010011111
• decimal to octl: solve all

  1. 5678
  2. 92923
  3. 23423
  4. 295
  5. 59672

  ANSWERS:

  1. 13056
  2. 265373
  3. 55577
  4. 447
  5. 164430
• Decmial to hexadecimal

  1. 59672 = E918
  2. 12345 = 3039
  3. 4568 = B26E
  4. 18456 = 4818
• Binary to decimal (use positional notation so memorize the powers of 2)

  1. 101110111 = 375
  2. 1111000111001 = 7737
  3. 1111111111111111 = 65535
  4. 10111001110011 = 11891
• Octal to decimal (memorize power of 8)

  1. 745 = 485
  2. 16474 = 7484
  3. 4567 = 2423
  4. 24325 = 10453
• hexadecimal to octal (memorize powers of 16)

  1. 1A3 = 419
  2. 2AB9 = 10937
  3. 4AFEB = 307179
  4. 9FFFF = 655359
• binary to octal

  1. 110101 = 65
  2. 1101011111 = 1537
  3. 11010111110111111 = 327677
  4. 1111110001111010101011 = 17617253
• Binary to hexadecimal

  1. 10111011 = BB
  2. 10111011000111 = 2EC7
  3. 1110110011011 = 1D9B
  4. 10101101010101111011 = AD57B
• Octal to Binary

  1. 1345 = 1011100101
  2. 234 = 10011100
• Octal to hexadecimal

  1. 7777 = FFF
  2. 5462 = B32
• hexadecimal to binary

  1. A145 = 1010000101000101
  2. FFFF = 1111111111111111
  3. FF29F = 11111111001010011111
  4. A9F62B = 101010011111011000101011
• Hexadecimal to octal

  1. FF = 377
  2. FF945 = 3774505
  3. 12389 = 221611
  4. FADBA = 3726672
• with decimals (dec to bin)

  99.4375 = 1100011.0111

  do the integerr normally but for decimal point:

  
• 123.6875 = 1100011.0111


  Do the integer normally but: