CS 1.4 Data

• Denary is base 10, Binary is base 2, Hexadecimal is base 16 - 0-F.
• Converting denary to binary: take away the largest power of 2 possible from your number and continue until 0.

  Converting denary to hexadecimal: convert into an 8 digit binary number, then split this number into 2 nibbles and convert the 2 nibbles to hexadecimal.

  Converting hexadecimal into binary: split the hexadecimal into 2, convert both into denary and then into binay.

  Converting binary into hexadecimal: split into 2, convert each nibble into denary and then into hexadecimal.

  Why use hexadecimal? Are more human friendly, and uses less digits.
• Data structure: A way of storing and manipulating data.
• Data Type: What type of value a variable has and how it must be treated.
• Array: A set of data items of the same type grouped together using a single identifier, it is static so the size cannot change and is base 0.
• Dimension: How many indexes it has, a 1D, 2D or 3D array.
• Records: Comprised multiple related attributes of different data types
• Lists: ordered set of data that is not static- fixed in size.
• Tuples: Immutable list - cannot be changed.
• Binary addition rules0+1 = 11+1 = 0 (carry 1)1+1+1 = 1 (carry 1)

  0+0 = 0
• Sign and Magnitude: Where the leftmost bit is 1 to represent a negative number or 0 to represent a positive number. This bit is NOT included when you add them up.
• Two's Complement: Where if the leftmost bit is a 1 it becomes a negative number and IS added in the calculations.
• Two's Complement to unsigned bits: Take the binary in TC and flip the bits. Add one.
• Denary to TC: Write the negative number as a positive one in binary, flip the bits and add one.
• Borrowing: During binary subtraction, when borrowing from the next number, you borrow 2 not 1.
• Negative subtraction: 6-7 is the same as 6+-7, so you can do addition.
• Binary subtraction rules1 - 1 = 00 - 0 = 00 - 1 = 1 (after carrying)

  1 - 0 = 1
• Bitwise OperationsLeft Shift:Multiplies by 2.Most significant bit is lost and 0 fills least significant bit.Right Shift:Divides by 2.Least significant bit is lost and 0 fills the most significant bit.Can lead to overflow errors.
• AND or & Both bits in the calculation must be 1 for the output to be 1

  OR or | Either bits can be one for the output to be one in this calculation.

  XOR or ^ Only one bit can be 1 for the output to be one.
• Bit Mask: A bit mask is data used with a bit wise operator.
• Karnaugh Maps: A method to simplify Boolean algebra expressions.
• Truth table Into Karnaugh Map:1.Put variables on Karnaugh grid.2.Write out inputs: 00 01 11 10.3.Where the expression is true, put a one in the grid.4.Fill in the 0s.5.Find the common variables where the ones are.6.Write out the expressions with OR between them.
• An adder is a logic circuit that is used for the addition of binary numbers.A binary half adder circuit adds two 1-bit binary numbers together. Is an XOR and AND gate.A full adder adds three 1-bit binary numbers together. I made of 2 half adders and a OR gate.They return a C(Carry-out)
• D-Type Flip Flop: Are used in S-RAM.A flip flop stores the value of a single bit.They are positive edge triggered, meaning that they can only change the output when the clock is at a rising edge.
• Absorption Laws:

  A Λ (A V B) = AA V (A Λ B) = A
• AND Laws:

  A ∧ 0 = 0A ∧ 1 = AA ∧ A = AA ∧¬A = 0
• Associative Laws:

  (A Λ B) Λ C = A Λ (B Λ C)(A V B) V C = A V (B V C)
• Commutative Laws:

  A Λ B = B Λ AA V B = B V A
• De Morgan's Laws:

  ¬(A Λ B) = (¬A V ¬B)¬(A V B) = (¬A Λ ¬B)
• Distributive Laws:

  A Λ (B V C) = ( A Λ B ) V (A Λ C)A V (B Λ C) = ( A V B ) Λ (A V C)
• Inversion Law:

  ¬¬A = A
• OR Laws:

  A ∨ 0 = AA ∨ 1 = 1A ∨ A = AA ∨¬A = 1