GATE CSE 1996 | Question: 2.21

Question

Consider the circuit in below figure which has a four bit binary number $b_3b_2b_1b_0$ as input and a five bit binary number, $d_4d_3d_2d_1d_0$ as output.

• A. Binary to Hex conversion

• B. Binary to BCD conversion

• C. Binary to Gray code conversion

• D. Binary to $radix-12$ conversion

Comments

What does 'φ' mean here ?

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SHI IT MEANS SHI

Answer 1

Whenever, $b_{2}$ = $b_{3}$$=$ $1$, then only $ 0100$ i.e., $4$ is added to the given binary number. Let's write all possibilities for $b$.

$${\begin{array}{|c|c|c|c|}\hline
\bf{b_3}&    \bf{b_2}&  \bf{b_1}&\bf{ b_0} \\\hline
0&0&0&0 \\ 0&0&0&1\\    0&0&1&0 \\    0&0&1&1 \\    0&1&0&0 \\   0&1&0&1  \\   0& 1&1&0 \\   0&1&1&1\\   1&0&0&0\\   1&0&0&1\\    1&0&1&0 \\    1&0&1&1 \\   1&1&0&0  \\   1& 1&0&1 \\   1&1&1&0\\ 1&1&1&1 \\\hline
\end{array}}$$

Note that the last $4$ combinations ($1100$, $1101$, $1110$, $1111$) leads to $b_{3}$ and $b_2$ as $1$. So, in these combinations only $0100$ will be added.

$1100$ is $12$
$1101$ is $13$
$1110$ is $14$
$1111$ is $15$
in binary unsigned number system.

$1100 + 0100 = 10000$.
$1101 + 0100 = 10001$ and so on.
This is conversion to radix $12$.

Correct Answer: $D$

Comments

Can i say:-

(1100) base 2 =(10000) base 12    ?

But if i convert both to decimal ,then these are not equal?

I think the result can be separated into two digits of radix 12.

1 digit is :- d4

2nd digit(LSB) :- do to d3,It will amke one digit.

If we consider it as one number as i mentioned above,then it is not radix 12. 

Please check once

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$d_3d_2d_1d_0$ represents the $4$ bit binary equivalent of least significant digit of $radix \  12$ and $d_4$ represent most significant digit of $radix \ 12.$

$Example - (1111)_2 = (15)_{10}$
$1111 +0100 = \underset{1}{\underbrace{1}}\underset{3}{\underbrace{0011}}=(13)_{12} = (15)_{10}$

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why we adding 4

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@VIDYADHAR SHELKE 1

Because when b3=b2=1, 0100 is added to input. The decimal value of 0100 is 4.

 

Answer 2

Hope this helps.. I tried the possible way to explain this question. Please, find the attached screen shot.

Comments

Beautifully explained! :)

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what is the meaning of Binary to Radix-12 conversion here .?

 

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We are converting from Binary to Base 12 number

Answer 3

Φ means nothing (we consider it as 0 or null)

So if we add number which is greater than or equal to 12 then it returns according to input

For example, 

For 0-11 it returns as it is

       12 it returns 0(0100+1100=0000)

       13 it returns 1(0100+1101=0001)

       14 it returns 2(0100+1110=0010)

       15 it returns 3(0100+1111=0011)

Answer is option D Binary to radix-12 conversion

Comments

what is the meaning of Binary to Radix-12 conversion here .?

 

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12 is in decimal if we convert it into radix or base 12 then

12|12

12|1        0

    |0        1

gives (10) in radix 12

So, how it is giving 0...plz clear it.

Answer 4

when b3b2 is 11 restore circuit to 0000..
it counts from 0 to 11 i.e. Radix 12 no ..
circuit used for  binary to radix 12 conversion..

Comments

I didnt understand... Can u please explain in some more detail.... I think the diagram is not complete.. Is it so?

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Could someone please give some detailed explanation ? Thanks in advance.

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@digvijay how can u say ?

illustrate brother ur idea.

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if we add 1100 to 0100 it will reset to zero it means it is acting as binary to radix-12 conversion  here