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Flashcards in Circuits Deck (13):
1

What's the difference between Combinatorial and Sequential Logic?

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

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

A + B = B + A
A . B = B . A

4

Associative laws for logic

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

5

Distributive laws for logic

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

6

Boolean Identities

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

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

8

Tri-State Buffers

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

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

10 x 13 =
1010 x 1101
Add all the partial sums

first partial: 0000a3a2a1a0 AND b0b0b0b0b0b0b0b0
second: 000a3a2a1a00 AND b1b1b1b1b1b1b1b1
etc...

12

Flip flops

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.

13

Synchronous and Asynchronous systems

Synchronous system: A clocked system in which all processes share the same clock signal. All outputs are held constant until the next time the flip-flops are clocked.

Asynchronous: The output of one process triggers the start of the next.