Flashcards in Circuits Deck (13):

1

## What's the difference between Combinatorial and Sequential Logic?

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Combinatorial logic: Generates output based solely on its current input.

Sequential logic: The output from a sequential logic element depends on its past history as well as its current input.

2

## Sum of products expression

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So just OR all the minterms (the AND of the variables that make the output 1)

Truth Table:

A B C F So the Sum of Products is

0 0 0 0 F = A'BC + AB'C + ABC

...

0 1 1 1

...

1 0 1 1

1 1 1 1

3

## Commutative laws for logic

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A + B = B + A

A . B = B . A

4

## Associative laws for logic

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(A . B) . C = A . (B . C)

A + (B + C) = (A + B) + C

5

## Distributive laws for logic

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A . (B + C) = A . B + A . C

(A . B) + C = (A + C) . (B + C)

6

## Boolean Identities

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AND: OR: NOT:

0.x = 0 0+x = x x'' = x

1.x = x 1+x = 1

x.x = x x+x = x

x.x' = 0 x+x' = 1

7

## DeMorgan's Theorem

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(A+B)' = A' . B'

(A.B)' = A' + B'

8

## Tri-State Buffers

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Enable Input Output

0 0 Floating

0 1 Floating

1 0 0

1 1 1

9

## The Sum of the Half Adder can also be written as

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XOR of the inputs

(A+B).(AB)'

10

## Depth of a circuit

### The largest number of gates on any path from an input to an output.

11

## Binary Multiplication

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10 x 13 =

1010 x 1101

Add all the partial sums

first partial: 0000a3a2a1a0 AND b0b0b0b0b0b0b0b0

second: 000a3a2a1a00 AND b1b1b1b1b1b1b1b1

etc...

12

## Flip flops

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RS Flip-Flop: Two inputs, R(eset), and S(et). R=S=1 is forbidden. It is a latch, used for recording events.

D Flip-Flop: Two inputs, D(ata) and C(lock). It records the state of D and holds it constant until C is clocked. It is used for memory elements such as registers.

JK Flip-Flop: Has three inputs, J(Set), K(Klear) and (C)lock. Output remains in previous state so long as it is not clocked. Works like RS flip-flop, but toggles if J=K=1.

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