Boolean Algebra

Question 1

Describe an AND Gate Truth Table

Answer 1

Question 2

Describe an AND Gate Symbol

Answer 2

Question 3

Describe an OR Gate Truth Table

Answer 3

Question 4

Describe an OR Gate Symbol

Answer 4

Question 5

Describe a NOT Gate Truth Table

Answer 5

Question 6

Describe a NOT Gate Symbol

Answer 6

Question 7

Describe a NAND Gate Truth Table

Answer 7

Question 8

Describe a NAND Gate Symbol

Answer 8

Question 9

Describe a NOR Gate Truth Table

Answer 9

Question 10

Describe a NOR Gate Symbol

Answer 10

Question 11

Describe a XOR Gate Truth Table

Answer 11

Question 12

Describe an XOR Gate Symbol

Answer 12

Question 13

Describe a XNOR Gate Truth Table

Answer 13

Question 14

Describe the examples of Boolean Algebra

Answer 14

• AND - A ^ B
• OR - A v B
• NOT - ¬A
• NAND - ¬ A ^ B
• NOR - ¬ A v B
• XOR - A ⊻ B
• XNOR - ¬ A⊻B

Question 15

Describe how you simplify a Karnaugh map

Answer 15

• Write your truth table as a Karnaugh map
• Highlight all of the 1s in the map with rectangles
• The larger the groups the better
• You can only group 1s with edges equal to a power of 2 (1,2 or 4) and waraparounds are included
• Using the highlights simpifiy the expression

Question 16

What is de Morgan’s Law

Answer 16

Break the line and change the size (Breaking a negation and changing the operation)

Question 17

What are the General Rules of Boolean Algebra

Answer 17

1. X ^ 0 = 0
2. X ^ 1 = X
3. X ^ X = X
4. X ^ ¬X = 0
5. X v 0 = X
6. X v 1 = 1
7. X v X = X
8. X v ¬X = 1

Question 18

What are the Commutative Boolean Algebra Rules

Answer 18

X ^ Y = Y ^ X

X v Y = Y v X

Question 19

What are the Associtaive Boolean Algebra Rules

Answer 19

X ^ (Y ^ Z) = (X ^ Y) ^ Z

X v (Y v Z) = (X v Y) v Z

If operation is the same you can switch the brackets

Question 20

What are the Distributive Boolean Algebra Rules

Answer 20

X ^ (Y v Z ) = (X ^ Y) v (X ^ Z)

(X v Y) ^ (W v Z) = (X ^W) v (X ^ Z) v (Y ^ W) v (Y ^ Z)

You can expand brackets

Question 21

What are the Absorption Boolean Algebra Rules

Answer 21

X v (X ^ Y) = X

X ^ (X v Y) = X

If operations are diffferent simply to the input that occurs twice

Question 22

What is the Double Negation Boolean Algebra Rule

Answer 22

¬¬X = X

Question 23

What is a flip flop

Answer 23

• A type of logic circuit that can store one bit and flip between two states, 0 and 1
• A flip flop has two inputs a control signal and a clock input
• A clock is a regular pulse generated by the CPU

Question 24

What is the D-type flip flop

Answer 24

• It stores 1-bit of data
• It is a positive edge-triggered flip-flop meaning that it can only change the output value from 1 or 0 when the clock is at a rising or positive edge (at the start of the clock period)
• When the clock is not at a positive edge, the input value is held and does not change

Question 25

What are D-type flip flops used for

Answer 25

* The D-type flip flop is made up of several NAND gates and is useful because they can be used as a memory cell to store the state of a bit * These flip flops can be made into register memories by connecting a series of flip flops in a row * They are typically used for intermediate storage needed during arthimetic operations * RAM is created using D-type flip flops

Question 26

What is an Adder

Answer 26

A logic circuit which adds together the number of inputs which are true, and outputs the number as a binary number

Question 27

What is a Half Adder

Answer 27

* A half adder can take an input of two bits and outputs the sum and carry of the two inputs * The circuit is formed from an AND and XOR logic gate

Question 28

What is a Full Adder

Answer 28

* Combines two half adders to add three bits together including a carry bit * The Full Adder is made from an ADD, XOR and NOR logic gate

Question 29

Describe how a half adder can be adapted to add together two 4-bit binary numbers

Answer 29

* A half adder adds together 2 binary digits * Two hald adders can be joined together with an OR gate * This will form a full adder, 4 full adders can be used to add 4 bit numbers * Carry out one joined to carry in on next