34822559
Description
Flashcards by Malachy Moran-Tun, updated more than 1 year ago
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Created by Malachy Moran-Tun
over 3 years ago
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| Question | Answer |
| Why do Computers use Binary Logic? | > Can only recognise the presence or absence of current (or voltage in the case of analogue electronics) > The voltage in a computer is measured as high or low - 1 or 0 > Electronic logic gates take these inputs and produce a single output, which can be used in later gates, allowing for complex circuits |
| What is a NOT Gate and its Symbol? | > Inverts the input > Q = ¬A > ¬1 = 0 and visa versa |
| What is an AND Gate and its Symbol? | > Outputs 1 only if both inputs are 1 > Q = A ∧ B > 1 ∧ 1 = 1 > 1 ∧ 0 = 0 > 0 ∧ 0 = 0 |
| What is an OR Gate and its Symbol? | > Outputs 1 only if any inputs are 1 > Q = A ∨ B > 1 ∨ 1 = 1 > 1 ∨ 0 = 1 > 0 ∨ 0 = 0 |
| What is an XOR Gate and its Symbol? | > Outputs 1 only if only one input is 1 > Q = A ⊻ B > 1 ⊻ 1 = 0 > 1 ⊻ 0 = 1 > 0 ⊻ 0 = 0 |
| What's the Benefit of Simplifying Boolean Expressions? | > Uses less components > More reliable > Faster > Generates less heat > Cheaper |
| *sigh*... What are the General Rules of Boolean Algebra? (8 of them) | 1. X ∧ 0 = 0 2. X ∧ 1 = 1 3. X ∧ X = X 4. X ∧ ¬X = 0 5. X ∨ 0 = X 6. X ∨ 1 = 1 7. X ∨ X = X 8. X ∨ ¬1 = 1 |
| What are the Commutative Rules of Boolean Algebra? (yes they are REALLY obvious) | 1. X ∧ Y = Y ∧ X 2. X ∨ Y = Y ∨ X |
| What are the Associative Rules of Boolean Algebra? | 1. X ∧ (Y ∧ Z) = (X ∧ Y) ∧ Z 2. X ∨ (Y ∨ Z) = (X ∨ Y) ∨ Z |
| What are the Distributive Rules of Boolean Algebra? (yes they're really damn long) | 1. (X ∧ Y) ∨ (X ∧ Z) = X ∧ (Y ∨ Z) 2. oh god... (X ∨ Y) ∧ (W ∨ Z) = (X ∧ W) ∨ (X ∧ Z) ∨ (Y ∧ W) ∨ (Y ∧ Z) :( |
| What are the Absorption Rules of Boolean Algebra? | 1. X ∨ (X ∧ Y) = X 2. X ∧ (X ∨ Y) = X |
| What is the Extremely Obvious, Hopefully Logically Oblivious, Extraordinarily Clear Double Negation Rule of Boolean Algebra? | 1. X = ¬¬X |
| What are de Morgan's Laws of Boolean Algebra? | 1. ¬(A ∧ B) = ¬A ∨ ¬B 2. ¬(A ∨ B) = ¬A ∧ ¬B |
| What are Karnaugh Maps? | > Provide an alternate way of simplifying boolean expressions > Often easier than using boolean algebra when manipulating many variables > Similar to truth tables > Allows for easy grouping of common factors |
| How do you Group Expressions for use in a Karnaugh Map? | Split at the OR (∨) e.g., (A ∧ B) ∨ C = (A ∧ B) ¦ C |
| How do you Fill in a Karnaugh Map? | > Mark where each variable would be 1 or 0 respectively, depending on the presence of ¬ (e.g., A = 1, ¬A = 0) > Match up the respective variable with the box(es) on the Karnaugh Map yes that's a bad explanation but oh well |
| What are the Rules for Simplifying Boolean Expressions in Karnaugh Maps? | > Group factors in boxes / squares > Boxes must contain 2ⁿ values > Do not use diagonals > Only 1s must be in the boxes > Boxes must be as large as possible > Boxes can overlap and wrap around |
| What are the Steps for Simplifying Boolean Expressions in Karnaugh Maps? | > Take each box in any order > Take each variable in any order > If the digit for the variable in the heading stays the same, keep it > Otherwise, discard the variable > Write down the simplified expression with OR / ∨ in between |
| What is a Half Adder? | > Takes an input of two bits and gives a two-bit output > The carry bit cannot be used from a previous addition as there are only two inputs |
| What is the Logic Diagram for a Half Adder? | S = A ⊻ B C = A ∧ B |
| What is a Full Adder? | > Combines two half adders to add 3 bits together > Includes three inputs: A, B, and a carry bit C > Gives a two bit output |
| What is the Logic Diagram for a Full Adder? | S = A ⊻ B ⊻ Cᵢₙ Cₒᵤₜ = (A ∧ B) ∨ (Cᵢₙ ∧ (A ⊻ B)) |
| How do you Connect Multiple Adders to Add more Bits? | > Use the carry from the first adder to the next |
| What is a Flip-Flop? | > Elemental sequential logic circuit (no i don't know what that means either) > Stores one bit > Flips between two states: 0 and 1 (wow!) > Two inputs: a control input and a clock signal |
| What is a Clock / Oscillator? | > Type of sequential circuit > Changes state at regular time intervals > Necessary to sync the change of state of flip-flops |
| What is a D-type Flip-Flop | > Positive edge-triggered flip-flop > Can only change the output value from 1 to 0, or visa versa, when the clock is at a rising / positive edge (when the clock is "going" from 0 to 1, not 1 to 0) > When the clock is not at a positive edge, the input value is held and does not change |
| What is the Symbol for a D-type Flip-Flop? | ▷ = positive edge-triggered clock signal |
| Why is the Flip-Flop Circuit Important? | Can be used as a memory cell to store the state of a bit |
| What are some Examples of a D-type Flip-Flop being used as a Memory Unit? | > Register memories, used for intermediate storage needed during arithmetic operations > Static RAM |
| have a timing diagram because idk how to make a flashcard out of it |
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