Chapter 4

Question 1

combinational circuit

Answer 1

consists of logic gates whose outputs are determined from only the present combination of inputs

Question 2

a combinational circuit performs an operation that can be specified logically either by ___________ or ___________

Answer 2

a set of boolean functions
truth table

Question 3

design procedure for combinational circuit

Answer 3

1. specification
2. formulation
3. optimization
4. verification

Question 4

specification

Answer 4

label input and output

Question 5

formulation

Answer 5

derive a truth table or boolean equations that define the relationship between the inputs and outputs

Question 6

optimization

Answer 6

use k map and draw a logic diagram

Question 7

verification

Answer 7

use CAD tools to verify the final design with simulation

Question 8

practical considerations of a combinational circuit

Answer 8

• number of gates
• max allowed delay
• max consumed power
• working conditions

Question 9

excess-3 code converter

Answer 9

add three to the number

Question 10

Half adder

Answer 10

addition of two bits, results in two outputs: sum and carry

Question 11

full adder

Answer 11

addition of three bits to account for carry bit from previous digit, results in two outputs: sum and carry

Question 12

ripple carry adder

Answer 12

aka binary adder - created by connecting cascading full adders
addition of n-bit numbers needs n full adders

Question 13

input carry of binary adder ________

Answer 13

is fixed at 0

Question 14

four-bit adder is an example of a _____________

Answer 14

standard component or modular design

Question 15

for an n-bit adder, there are ____ gate levels for the carry to get from input to output

Answer 15

2n

Question 16

binary subtractor basic principal

Answer 16

for unsigned binary numbers, take the 2’s complement of subtrahend and add them together

Question 17

binary subtractor gate explanation

Answer 17

for A-B:
- each digit of B is xored with an extra input (M) to take 2’s complement before entering the FA
- M is 1 for subtraction, 0 for addition
- M is also the carry input for the first digit

Question 18

Decoder

Answer 18

• converts binary information from n input lines to a max of 2^n unique output lines
• at any time there will be exactly one output set to 1, the rest are 0

Question 19

enable input of decoder

Answer 19

• En
• controls encoder operation so that when En=0, there is no output and when its 1 the decoder functions as normal

Question 20

DECODER: if you have 3 inputs (x0,x1,x2) and 8 outputs (y0…y7) what would first line of truth table look like

Answer 20

x2 x1 x0 y0 y1 y2 y3 y4 y5 y6 y7
0 0 0 1 0 0 0 0 0 0 0

Question 21

how do you create a full adder from a half adder

Answer 21

input x and y go to first HA, then sum1 and z go into second half adder, sum2 = final sum and carry1 is ored with carry2 to get final carry

Question 22

applications of decoders

Answer 22

1. selection of peripheral devices - select/deselect things like hard disk, cd drive etc
2. instruction decoder - computer programs based on instructions that are decoded by the computer hardware and implemented

Question 23

how can any combinational circuit be implemented with a decoder

Answer 23

for n inputs and m outputs, use n to 2^n decoder and m OR gates
- can be used since boolean function can be expressed in standard sop form
- all minterms that satisfy one output variable are ored

Question 24

encoder description

Answer 24

• performs inverse operation of a decoder
• 2^n inputs and n outputs
• assumed only one input has a value of 1 at a time

Question 25

encoder gate description

Answer 25

• find truth table for outputs
• each output is gotten by oring all inputs that result in that output being 1

Question 26

priority encoder

Answer 26

• has priority for if more than 1 input is 1 at a time

Question 27

would y3 or y0 have higher priority in an encoder

Answer 27

y3

Question 28

what is the third output of a priority encoder

Answer 28

V - valid bit indicator
set to 1 when one or more inputs are equal to 1, if all inputs are 0, V is 0

Question 29

when are the outputs of a priority encoder dont cares

Answer 29

when V=0 the other outputs are not inspected

Question 30

multiplexer description

Answer 30

• 2^m to 1 multiplexer has 2^m inputs and m select inputs

Question 31

select inputs

Answer 31

used in multiplexer to route data from 2^m inputs to the single output

Question 32

multiplexer reminder 2 to 1

Answer 32

f = s’w0 + sw1
so when s is 0, w0 occurs
when s is 1, w1 occurs

Question 33

4 to 1 MUX truth table

Answer 33

s0 s1 f
0 0 w0
0 1 w1
1 0 w2
1 1 w3

Question 34

draw a 2 to 1 multiplexer

Answer 34

just do it - its lecture 19 slide 23

Question 35

a multiplexer is essentially __________

Answer 35

a decoder that includes the OR gate within the unit

Question 36

demultiplexer

Answer 36

• can deliver multiple outputs from a single inputs

Question 37

the data/ input to a demux ______

Answer 37

must be 1 to create any outputs

Question 38

the outputs of a demux are controlled by ________

Answer 38

1st - data must be 1
2nd - uses n control inputs to decide which of 2^n outputs occurs

Question 39

digital comparator

Answer 39

• compares the values of two inputs (greater than, less than, or equal)

Question 40

2 types of digital comparators

Answer 40

identity comparator
magnitude comparator

Question 41

identity comparator

Answer 41

only one output, if A=B, then output is one, otherwise its zero

Question 42

magnitude comparator

Answer 42

three output terminals, one for each type of equality

Question 43

boolean expression for A<B

Answer 43

A’B

Question 44

boolean expression for A>B

Answer 44

A’B

Question 45

boolean expression for A=B

Answer 45

(A’B+B’A)’

Question 46

multi bit comparators

Answer 46

use n cascading comparators to compare n-bit values