Q.Convert $(1001)_G$ into binary using X-OR gates.

The Gray code is a special non-weighted binary code whose most important feature is that only one bit changes when moving from any value to the next. Because of this unit-distance property, Gray code is also called the reflected binary code, and it is widely used in shaft encoders, rotary position sensors and other systems where a single miscounted bit during a transition could cause a large, dangerous error.

To convert binary to Gray, the most significant bit of the Gray code equals the most significant bit of the binary number; each remaining Gray bit is the XOR of the corresponding binary bit and the binary bit just to its left. In equation form, $G_i = B_{i+1} \oplus B_i$. For example $1101_2$ becomes $1011$ in Gray code. …