Code Converter

 

The code converters are logic circuits used to perform the operation of converting the information into the code which we want. Code conversion is basically performed by encoder, decoder and code converter circuit which converts the data into an encoded form.

Code conversion takes place in every device in which input values are entered into a system for processing. Code conversion is needed to operate the electronic displays that show numbers or letters on calculators and clocks.

Binary to Gray converter

The Gray code is a reflected code which has the property that two consecutive numbers differ through the value of a single bit. Both binary and gray codes are listed below according to each others correspondence. The table below can be considered as the converter truth table.

From the above table we can build the K-Map for and find the boolean expressions: 

The boolean expressions of the 4 outputs are obtained:

G₀ = B₀⊕B₁

G₁ = B₁⊕B₂

G₂ = B₂⊕B₃

G₃ = B₃

From these equations we can obtain the logic circuit of a binary to gray code converter: 

Gray to binary converter

Using the same algorithm as we have used in binary to gray converter, we can obtain the circuit for gray to binary converter. We have to just find the boolean expressions for Binary outputs by processing the above expressions:

G₃ = B₃ => B₃ = G₃

G₂ = B₂⊕B₃ => G₂⊕G₃ = B₂⊕B₃⊕B₃ = B₂ =>  B₂ = G₂⊕G₃

G₁ =  B₁⊕B₂ => G₁⊕G₂⊕G₃ = B₁⊕B₂⊕B₂ = B₁ => B₁  = G₁⊕G₂⊕G₃

G₀ = B₀⊕B₁ => G₀⊕G₁⊕G₂⊕G₃ = B₀⊕B₁⊕B₁ = B₀ => B₀ = G₀⊕G₁⊕G₂⊕G₃ 

These expressions help us in making the logic circuit of gray to binary converter which is given below: