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[ 1.4.3 ]

1

what are the two possible outputs of a **boolean** equation?

** True or False** (or 1/0)

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2

why do we use **karnaugh maps**?

to __simplify boolean expressions__

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3

how do you **find** the simplified expression from a completed **karnaugh map**?

take each box in any order

take each variable in any order

if the digit for the variable in the heading

,__stays the same__the variable__keep__if the digit for the variable in the heading

,__changes__the variable__discard__

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4

what are the **8** rules for drawing **boxes** on a **karnaugh map**?

boxes must be

or__rectangles____squares__boxes__no diagonal__boxes must

__only contain 1s__boxes must be

__as large as possible__boxes can only be made of

**2**1s ( e.g 1, 2, 4, 8 etc)^{n}boxes

__can overlap__use the

__smallest amount of boxes possible__boxes can

the edges of the map__‘wrap around’__

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5

why do we **simplify** boolean expressions?

decreases considerably the

__cost of the hardware__by the chip__reduces the heat generated__most importantly,

__increases speed__

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6

**de morgan’s laws**

¬(A V B) ≡ ¬A Λ ¬B

¬(A Λ B) ≡ ¬A V ¬B

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7

**distribution**

A V (B Λ C) ≡ (A V B) Λ (A V C)

A Λ (B V C) ≡ (A Λ B) V (A Λ C)

*note that this works for __only AND____ and __** only OR** as well

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8

**association**

(A Λ B) Λ C ≡ A Λ (B Λ C) ≡ A Λ B Λ C

(A V B) V C ≡ A V (B V C) ≡ A V B V C

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9

**commutation**

A V B ≡ B V A

A Λ B ≡ B Λ A

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10

**double negation**

¬¬A ≡ A

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11

**absorption**

A Λ (A V B) ≡ A

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12

draw the **truth table** and **symbol** for the logic gate **AND**.

**Λ**

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13

draw the **AND** gate and describe it’s function.

applied to two literals to produce one output

only outputs true (1) when

__both literals are true__can be thought of as applying

to its inputs__multiplication__

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14

draw the **truth table** and **symbol** for the logic gate **OR**.

**V**

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15

draw the **OR** gate and describe it’s function.

applied to two literals to produce one output

outputs true (1) when

__one or more literals are true__can be thought of as applying

to its inputs__addition__

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16

draw the **truth table** and **symbol** for the logic gate **NOT**.

**¬**

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17

draw the **NOT** gate and describe it’s function.

applied to

(input) to produce a single output__one literal__the value of the input__‘flips‘__

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18

draw the **truth table** and **symbol** for the logic gate **XOR**.

**⊻**

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19

draw the **XOR** gate and describe it’s function.

applied to two literals (inputs) to produce a single output

similar to

, differs when both inputs are true__OR__only outputs true when

input is true__exactly one__

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20

describe a **half-adder** and **draw** the circuit.

a logic circuit that

together__adds two bits__outputs a digit (sum) and a carry bit (remainder)

does not provide input for a carry bit from a previous addition

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21

describe a **full-adder** circuit and its **function**.

a logic circuit that adds

(Cin) together__two bits, and a carry bit__outputs a digit (sum) and a carry bit (remainder)

can be

together (e.g a byte) by__combined to add larger numbers____feeding the carry bit of the previous addition into the next__

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22

describe a **D type flip-flop** and it’s **function**.

a logic circuit that

__stores the state of a bit____,__and can ‘flip’ between 0 and 1it has two inputs:

(D) and a__a single bit data input____clock signal__the output of the circuit (Q) only changes when the clock pulse is at a

__rising edge__when this occurs the output is changed to the value of D

__at that moment__

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