Binary to radix-12 conversion

Consider the circuit in Fig.2.21 which has a four bit binary number b3b2b1b0 as input and a five bit binary number, d4d3d2d1d0 as output.

  1. Binary to Hex conversion

  2. Binary to BCD conversion

  3. Binary to grey code conversion

  4. Binary to radix-12 conversion

Can anyone explain how this circuit convert binary to radix-12 conversion.

Ashish Kumar Goyal @dashish
28 Jan 2017 12:23 pm

Its clear that Φ=b3.b2 and Cin is Φ. what does the second input to adder consists of?? is it's all bits Φ or only the last bit Φ or anything else??

Shraddha @shraddhagami
28 Jan 2017 02:53 pm

My doubt is clear now


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=0001)

Ashish Kumar Goyal @dashish
30 Jan 2017 08:34 pm


where does that 0100 come from??

Shraddha @shraddhagami
30 Jan 2017 09:41 pm


 b2 and b1 are given to 'And' gate

Output of 'And' Gate are given to 2nd input of first 4 input.

Ashish Kumar Goyal @dashish
31 Jan 2017 09:51 am

Ok now i see! the diagram in the question is wrong..

correct one in comment.. totally fine