How i can Convert the gray code 110111101 to binary code and design the circuit?

first decide the numbar of bits...for four bits write the varoiurs combination of each bit.

for 4 bits 2^4=16 combination starting from 0000-1111.

similarly you will get 4 bit gray code by ex-oring (u may find this conversion in any book digital book).

now draw k-map for each out put bit

binary gray

0000 0000

0001 0001

0010 0011

...... ......

....... ......

1111 0000

consider case for 0010 to 0011.

lsb will be g0(1) and msb will be g3.(0)

each bit should be considered as an output and k-map has to be drawn for each output,viz g0,g1,g2,g3.

after implementing this ,realise the output expression using gates.(k map will give simplified output).

this is basic operation...but if u plan to implement in an project try getting an ready made IC.