The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+12 votes
901 views
  1. Is the $3\text{-variable}$ function $f= \Sigma(0,1,2,4)$ its self-dual? Justify your answer.
  2. Give a minimal product-of-sum form of the $b$ output of the following $\text{excess-3}$ to $\text{BCD}$ converter.

asked in Digital Logic by Veteran (59.7k points)
edited by | 901 views
0
plz answer part B also..
+1
$Remark:$ self dual function is that function, if we calculate one time dual of that function then we get the original function back.

5 Answers

+17 votes
Best answer

There are two condition for a function being self dual.

1- it should be neutral function. (no. of minter = no. of max term)

2-no mutually two exclusive term should be there like $($$0-7$ are mutually exclusive $1-6, 2-5, 3-4$$)$ from these pairs only one should be there.
Clearly, there are $4$ minterm, so number of minterms = no. of maxterms.
and second condition is also satisfied. So, it is a self dual function .

b) excess-3 to BCD
 

answered by Boss (16k points)
edited by
0
why 0,1,2 are taken as dont care??

i got the reason why 13,14,15 are taken as dont care ,as 13+3=16 cant be represented in 4 bits, thats the reason for 14,15 too.
+14 votes

checking self dual of a function.

f=Σ(0,1,2,4) = a'b'c' + a'b'c + a'bc' + ab'c' 

now write it in max term form (a'+b'+c')(a'+b'+c)(a'+b+c')(a+b'+c')

                                                        7             6             5           3

         =$\prod$(3,5,6,7) =$\sum$(0,1,2,4) = given function so its a self dual

answered by Boss (16.1k points)
+4 votes

part b

thanks :)

answered by (451 points)
+4 votes

(b) Excess-3 to BCD 

Minimal product of sum (b4, b3, b2, b1)

answered by (273 points)
+1 vote

a) It is a self dual function, because it satisfies both conditions of self dual fuction

            ->It should be neutral (i.e no. of minterms is equal to the no. of maxterms)

            ->The function does not contain two mutually exclusive term ( eg ABC mutually exclusive to A'B'C' , AB'C' mutually  excluseive to A'BC)


b) Excess-3 to BCD converter

 Ref http://www.sukanta.info/wp-content/uploads/2012/05/Excess-3-code-to-bcd-converter3.pdf

answered by (335 points)

Related questions



Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

44,317 questions
49,814 answers
164,543 comments
65,866 users