Answer / aamod joshi

Lets assume that the weights are w1,w2,w3 and w4.

Assume the first code is X1X2X3X4 and second number is
Y1Y2Y3Y4 where X1X2X3X4 + Y1Y2Y3Y4 = 9. e.g. if the weights
are 2,4,2,1 then 1011 = (1*2)+(0*4)+(1*2)+(1*2) = 5 and
0100 = (0*2)+(1*4)+(0*2)+(0*2)= 4 i.e. 1011+0100=4+5=9.

Putting this in mathematical equation,
(W1X1 + W2X2 + W3X3 + W4X4)
+ (W1Y1 + W2Y2 + W3Y3 + W4y4)
= 9

Which means
W1(X1+Y1) + W2 (X2+Y2) + W3 (X3+Y3) + W4 (X4+Y4) = 9

Now, as X1X2X3X4 and Y1Y2Y3Y4 are self-complementing, at a
time either of X1 and Y1 can be 1, the other will be zero.
Same for X2,Y2 and X3,Y3 and X4,Y4. Which further means
that X1+Y1 = 1, X2+Y2=1, X3+Y3=1, X4+Y4=1.

So,
W1(1) + W2(1) + W3(1) + W4(1) = 9

i.e. W1+W2+W3+W4 = 9 thus it proves that sum of the weights
has to be 9.

Answer / nobody

In self complementing code, 9's complement in decimal is the
1's complement in binary.

Now, assume a code with weights are W1,W2,W3 and W4.

We want to prove that,
W1 + W2 + W3 + W4 = 9

Let 'N' be a number in decimal.

Let N's binary equivalent in given code be
X1X2X3X4

Lets represent complement of N as COMP(N).

Let COMP(N)'s binary equivalent in given code be
Y1Y2Y3Y4

Therefore,

N = W1(X1) + W2(X2) + W3(X3) + W4(X4) ***************[1]

Now 9's complement of N is
[9's COMP(N)] = 9 - N
[9's COMP(N)] = 9 - [W1(X1) + W2(X2) + W3(X3) + W4(X4)]
***** (from eq.1) *******[2]

Now, COMP(N)'s binary equivalent in given code is Y1Y2Y3Y4.
COMP(N) = W1(Y1) + W2(Y2) + W3(Y3) + W4(Y4)
********************[3]

Now as it is a self complementing code, 9's complement in
decimal is equal to the 1's complement in binary.

Therefore,

[9's COMP(N)] = COMP(N)

From [2] and [3]

9 - [W1(X1) + W2(X2) + W3(X3) + W4(X4)] = W1(Y1) + W2(Y2) +
W3(Y3) + W4(Y4)

[W1(X1) + W2(X2) + W3(X3) + W4(X4)] + [W1(Y1) + W2(Y2) +
W3(Y3) + W4(Y4)] = 9

W1(X1+Y1) + W2(X2+Y2) + W3(X3+Y3) + W4(X4+Y4) = 9
****************************[4]

Now, as (X1,Y1) (X2,Y2), (X3,Y3), (X4,Y4) are complements of
each other, their sums will always be 1.
i.e
(X1 + Y1) = (X2 + Y2) = (X3 + Y3) = (X4 + Y4) = 1.

Putting this in eq. [4], we get,

W1(1) + W2(1) + W3(1) + W4(1) = 9

i.e
W1 + W2 + W3 + W4 = 9

Answer / dp

It is related to Digital Logic Design

Answer / vivek

I really dint understand this question or the answer. can u
please tell me which subject is this question related to ??

Answer / poojitha

In general 2421,5211,642-3,84-2-1 and excess-3 codes are satisfies the condition of self complementing code.All the above codes gives sum as 9 as shown below:
2+4+2+1=9
5+2+1+1=9
6+4+2-3=9
8+4-2-1=9
so,in the self complementing code sum of all weights is always 9.

Answer / munjal

if I am talking about 8421 code , then the sum must be 15 ,,
the question is limited to only 2421 code......

Answer / ankit agrawal

the sum of the number and its complements should be 9999

how to join the pc to the domain?

1 Answers   Aegis, jetking,

hi ,,,,I m going to attend corporate bank exam of specialist IT officer, I don't Know What type of question arise in interview..some suggest me my email id is surinder.singh.btech@gmail.com

0 Answers   State Bank Of India SBI,

1. what is the opportunity in hardware & networking in future? 2.how many courses r in networking that fulfill market requrment? 3.who is better for career MCSE or CCNA ,UNIX ?

0 Answers  

One of your responsibilities will be to prepare and train on standard work instructions or quality initiatives. What experience and qualifications do you have that will enable you to succeed in this role?

0 Answers  

what is the significance of partial derivatives.

1 Answers   MPSC, TCS,

What are the duties of QA/QC Coordinator

0 Answers  

please send aptitude test papers for reference with answers

0 Answers   ZenQ,

Whatis Bandwidth?

2 Answers   Elgi Equipments,

What is the meaning of "co relation" and what is the value of "co relation" in the performance testing environment.

0 Answers  

What is the procedure for taking leave while detecting Epf and Esi?

0 Answers  

i m doing engg in IT .for getting job which courses i have to do?

0 Answers   HCL,

hi........ i am a student of computer science. i want to earn some money on net so that i can help my parents. so please suggest me some sites which give online part time jobs without any registration charges. please help me. i will be very thankful to you. varinder.

1 Answers