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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.

1. Binary to Hex conversion

2. Binary to BCD conversion

3. Binary to Gray code conversion

4. Binary to $radix-12$ conversion

What does 'φ' mean here ?
SHI IT MEANS SHI

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$121101$is$131110$is$141111$is$15$in binary unsigned number system.$1100 + 0100 = 10000$.$1101 + 0100 = 10001$and so on. This is conversion to radix$12$. Correct Answer:$D$by ### 4 Comments edited 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$d_3d_2d_1d_0$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}\$

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

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

thanks!!
Beautifully explained! :)

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

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)

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

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

12|12

12|1        0

|0        1

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

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

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

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