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A Level Comp Sci Paper 1 > 1.4.3 Boolean Algebra > Flashcards

1.4.3 Boolean Algebra Flashcards

1
Q

What is this gate, what are the rules and what is the truth table associated?

A
  • AND gate
  • Both inputs must be on for the output to be 1
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2
Q

What is this gate, what are the rules and what is the truth table associated?

A
  • OR gate
  • 1 input must be on for the output to be on
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3
Q

What is this gate, what are the rules and what is the truth table associated?

A
  • XOR gate
  • If both inputs are on or off, the output is 0
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4
Q

What is this gate, what are the rules and what is the truth table associated?

A
  • NOT gate
  • It reverses the input
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5
Q

What is the main reason for using binary and name examples?

A
  • Easy to build electronic circuits with just 2 states:
    • RAM: Voltage or no voltage
    • Hard Disks: Polarity
    • Optical: Pits and lands
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6
Q

What is the symbol used for NOT and what is a rule with this?

A
  • ¬
  • Negation
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7
Q

What is the symbol used for AND and what is the rule associated?

A
  • ∧
  • Conjunction
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8
Q

What is the symbol used for the OR gate and what is the rule associated?

A
  • ∨
  • Disjunction
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9
Q

What is the symbol for the XOR gate and what is the rule associated?

A
  • Exclusive Disjunction
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10
Q

Exam Question: What is the difference between an OR and an XOR gate?

A
  • OR gate outputs true if at least 1 of its inputs is true.
  • XOR gate outputs true if one and only 1 of its inputs are true.
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11
Q

What is the Boolean Expression for this?

A
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12
Q

What is the Boolean expression for this?

A
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13
Q

Why is important to use as few expressions as possible?

A
  • Reduce the size of the circuit
  • Reduce the cost of manufacturing
  • Reduce the power consumption
  • Execute instructions as quickly as possible, reducing the need to fetch variables from memory
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14
Q

What does the Karnaugh map illustrate

A

B is false

The expression is NOT B (¬B)

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15
Q

What does this Karnaugh map illustrate?

A
  • A is true and B is true
  • A ∧ B
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16
Q
A
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17
Q
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18
Q

What are some rules on the boxes in Karnaugh maps?

A
  • Boxes must be rectangles or squares
  • No diagonal boxes
  • Boxes can only contain 1s
  • Boxes must be as large as possible
  • Boxes can overlap
  • Smallest possible number of boxes
  • Boxes must be 2n = 1, 2, 4, 8, 16
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19
Q
A
20
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21
Q
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22
Q
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23
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24
Q
A
25
Q

What are the rules and laws of Boolean simplification?

A
  • De Morgan’s law
  • Distribution
  • Association
  • Commutation
  • Double Negation
26
Q

What is De-Morgan’s Law

A
  • Way of simplifying Boolean expressions by inverting all the variables ANDs and ORs and vice versa and inverting the whole expression
27
Q

What is the answer to these:

  1. X ∧ 0
  2. X ∧ 1
  3. X ∧ X
  4. X ∧ ¬X
  5. X ∨ 0
  6. X ∨ 1
  7. X ∨ X
  8. X ∨ ¬X
A
  1. 0
  2. X
  3. X
  4. 0
  5. X
  6. 1
  7. X
  8. 1
28
Q

What are the 2 versions of the De Morgan’s Law?

A
  • First Law: NOT (A AND B) is the same as (NOT A) OR (NOT B)
  • Second Law: NOT(A OR B) is the same as (NOT A) AND (NOT B)
29
Q

How do you apply the De Morgan’s Law, what are the rules?

A
  1. Change OR to AND (or vice versa)
  2. NOT the terms on each side of the operator
  3. Invert result by adding NOT to everything that has changed
  4. Get rid of any double negation and unnecessary brackets
30
Q

Apply De Morgan’s Law on this expression:
¬(A V B)

A
  1. ¬(A ∧ B)
  2. ¬(¬A ∧¬B)
  3. ¬¬(¬A ∧ ¬B)
  4. ¬A ∧ ¬B
31
Q

What is Double Negation?

A
  • If you reverse something twice you get back to what you started
32
Q

What is Association?

A
  • To remove brackets from an expression and regroup variables
33
Q

What is Commutation?

A
  • The order of application of 2 separate terms is not important
  • A V B is the same as B V A
34
Q

What is Distribution?

A
  • Allows us to multiply or factor out an expression
  • A ∧ (B V C) is the same as (A ∧ B) V (A ∧ C)
35
Q

What is the logical circuitry called when using Binary Addition?

A
  • Half and Full Adders
36
Q

What is the process of producing a Half Adder?

A
  • Adding 2 numbers (A and B) together will produce 2 outputs, Digit and Carry bit out (C out)
  • Consider both the digit and Carry bit out separately. This produces an XOR and AND gate
  • Then add them together into a circuit
37
Q

What is the process of producing a Full Adder?

A
  • Instead of only considering 2 digits, consider 3 (A, B, and Cin (Carry bit in)
  • Use the first half adder and label the output X
  • Use 2nd half adder and add X with Cin to give digit
  • They have created a carry bit - this must be fed into the next calculation
38
Q

What is conjunction and disjunction?

A
  • Conjunction: Both sides of the proposition must be true
  • Disjunction: Either side of the proposition must be true
39
Q

What is negation and implication?

A
  • Negation: Reverse the truth of a proposition
  • if something is true, we can infer that something else is also true
40
Q

Why are flip flops required?

A
  • Full adders provide us with important processing functions but don’t allow us to maintain a state
  • As well as performing calculations, computers must be able to store and recall values
  • They need to preserve data over time, flip - flop is used
41
Q

What is a flip flop?

A
  • Fundamental logic circuit that can store 1 bit and flip it between 1 and 0
  • Has 2 inputs - a single bit data input (D) and a clock signal (C) - clock signal provided by another circuit that changes state at time intervals
  • Has 2 outputs - a single bit data output (Q) and the inverse of the data output (¬Q)
42
Q

What type of gate does a Flip-Flop use?

A
  • NAND gates
  • (NOT AND) - reverse the output of AND gates
43
Q

Why is a D-type flip flop a positive edge triggered circuit?

A
  • The output can only be changed when the clock pulse is at rising or positive edge
  • If the clock is not rising or positive edge, the output value is held and does not change
44
Q

How does a D-Type Flip-Flop store values?

A
  • The clock pulses are at regular intervals. There is a delay between high 1 and low 0s
  • A D type flip-flop circuit only receives high signal at the rising edge - the circuit perceives its input more accurately from the clock changing states
  • Small fraction that signal reads 1 before falling back to 0, only takes reading at rising edge
45
Q

How do D type - Flip-flops maintain values?

A
  • The single bit data input is set to 0
  • The clock pulse is high and is at its rising edge
  • Output of Q is 0
  • Output of NOT Q is 1
46
Q

Summarise a D-type flip flop:

A
  • Circuit used as a memory unit for registers and static memory to hold the state of a single bit
  • 2 inputs: D and clock input
  • At rising edge, output of Q is set to current value in D
  • Q will remain static and locked in place - even if D changes until the next clock pulse (rising edge)
47
Q

Exam Question:

State the purpose of a flip-flop (1)

A
  • To store the state of a bit

A Level Comp Sci Paper 1 (16 decks)

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