Circuits

Question 1

What’s the difference between Combinatorial and Sequential Logic?

Answer 1

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.

Question 2

Sum of products expression

Answer 2

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

Question 3

Commutative laws for logic

Answer 3

A + B = B + A

A . B = B . A

Question 4

Associative laws for logic

Answer 4

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

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

Question 5

Distributive laws for logic

Answer 5

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

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

Question 6

Boolean Identities

Answer 6

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

Question 7

DeMorgan’s Theorem

Answer 7

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

Question 8

Tri-State Buffers

Answer 8

Enable   Input     Output
 0             0         Floating
 0             1          Floating
 1              0              0
 1              1               1

Question 9

The Sum of the Half Adder can also be written as

Answer 9

XOR of the inputs

(A+B).(AB)’

Question 10

Depth of a circuit

Answer 10

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

Question 11

Binary Multiplication

Answer 11

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

first partial: 0000a3a2a1a0 AND b0b0b0b0b0b0b0b0

second: 000a3a2a1a00 AND b1b1b1b1b1b1b1b1
etc. ..

Question 12

Flip flops

Answer 12

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.

Question 13

Synchronous and Asynchronous systems

Answer 13

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.