Perform the following gray code to binary code
conversion (001) gray = (?)Binary
Construct the logic circuit for 3 bit gray to binary conversion.
Answers
Answer:
In computers, we need to convert binary to gray and gray to binary. The conversion of this can be done by using two rules namely binary to gray conversion and gray to binary conversion. In the first conversion, the MSB of the gray code is constantly equivalent to the MSB of the binary code. Additional bits of the gray code’s output can get using EX-OR logic gate concept to the binary codes at that present index as well as the earlier index. Here MSB is nothing but the most significant bit. In the first conversion, the MSB of the binary code is constantly equivalent to the MSB of the particular binary code. Additional bits of the binary code’s output can get using EX-OR logic gate concept by verifying gray codes at that present index. If the present gray code bit is zero then after that copy earlier binary code, as well copy reverse of earlier binary code bit. This article discusses an overview of code converters which includes binary to gray code converter as well as gray to binary code converter.
Gray Code to Binary Code conversion
G = G₂G₁G₀ (3-bit)
B = B₂B₁B₀ (3-bit)
To convert :
B₂ = G₂
B₁ = B₂⊕G₁
B₀ = B₁⊕G₀
Example 1 :
(001)gray = (?)binary
To convert :
B₂ = G₂ = 0
B₁ = B₂⊕G₁ = 0⊕0 = 0
B₀ = B₁⊕G₀ = 0⊕1 = 1
B = 001
Example 2 :
(100)gray = (?)binary
G = 1 0 0
B₂ = G₂ = 1
B₁ = B₂⊕G₁ = 1⊕0 = 1
B₀ = B₁⊕G₀ = 1⊕0 = 1
B = 111
Truth Table :
G₂G₁G₀ B₂B₁B₀
0 0 0 0 0 0
0 0 1 0 0 1
0 1 0 0 1 1
0 1 1 0 1 0
1 0 0 1 1 1
1 0 1 1 1 0
1 1 0 1 0 0
1 1 1 1 0 1
