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Binary to Gray & Gray to Binary CC

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Jaimin@prt.ltd.
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This document provides information about converting between binary and gray codes. It includes tables that show the binary and gray code equivalents for all combinations of bits from 0 to 1. It also shows the logic equations derived from K-maps to perform the conversions. The conversions are: Binary to Gray: G3=B3, G2=B3⊕B2, G1=B2⊕B1, G0=B1⊕B0 Gray to Binary: B3=G3, B2=G3⊕G2, B1=(G3⊕G2)G1⊕(G3⊕G2)G1, B0=G3

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Gandhinagar Institute of Technology Topic : Binary To Gray & Gray To Binary CC Degital Electronics ( 2131004 ) Active Learning Assignment Prepared by : Jaimin Darji (150120116013) GUDED BY: - Prof. Jatin Chakravti Branch : IT Division : A(A1)
Binary To Gray CC B3 B2 B1 B0 G3 G2 G1 G0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0
K-Map B1, B0 B1, B0 B3, B2 00 01 11 10 B3, B2 00 01 11 10 00 00 G3 = 01 G2= 01 11 11 10 10 B3 = G3 G2= B3 B2 + B3 B2 B1, B0 B1, B0 =B3 + B2 B3, B2 00 01 11 10 B3, B2 00 01 11 10 G1= 00 00 01 G0= 01 11 11 10 10 G1= B2 B1 + B2 B1 G0 = B1 B0 + B1 B0 = B2 + B1 = B1 + B0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
B3 G3 B2 G2 B1 G1 B0 G0
Gray To Binary CC G3 G2 G1 G0 B3 B2 B1 B0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0
K-Map G1, G0 G1, G0 G3, G2 00 01 11 10 G3, G2 00 01 11 10 00 00 B3= 01 B3=G3 B2= 01 11 11 10 10 G1, G0 B2= G3 G2 + G3 G2 G3, G2 00 01 11 10 = G3 + G2 00 B1= G3 G2 G1 + G3 G2 G1 + G3 G2 G1 + G3 G2 G1 B1= 01 = (G3 G2 + G3 G2) G1 + (G3 G2 + G3 G2) G1 11 = (G3 + G2) G1 + (G3 + G2) G1 10 = (G3 + G2) (G1 + G1) = G3 + G2 + G1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
G3 B3 G2 B2 G1 B1 G0 B0
Thank You!!!

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Binary to Gray & Gray to Binary CC

  • 1. Gandhinagar Institute of Technology Topic : Binary To Gray & Gray To Binary CC Degital Electronics ( 2131004 ) Active Learning Assignment Prepared by : Jaimin Darji (150120116013) GUDED BY: - Prof. Jatin Chakravti Branch : IT Division : A(A1)
  • 2. Binary To Gray CC B3 B2 B1 B0 G3 G2 G1 G0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 1 0 0 0
  • 3. K-Map B1, B0 B1, B0 B3, B2 00 01 11 10 B3, B2 00 01 11 10 00 00 G3 = 01 G2= 01 11 11 10 10 B3 = G3 G2= B3 B2 + B3 B2 B1, B0 B1, B0 =B3 + B2 B3, B2 00 01 11 10 B3, B2 00 01 11 10 G1= 00 00 01 G0= 01 11 11 10 10 G1= B2 B1 + B2 B1 G0 = B1 B0 + B1 B0 = B2 + B1 = B1 + B0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  • 4. B3 G3 B2 G2 B1 G1 B0 G0
  • 5. Gray To Binary CC G3 G2 G1 G0 B3 B2 B1 B0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 1 0
  • 6. K-Map G1, G0 G1, G0 G3, G2 00 01 11 10 G3, G2 00 01 11 10 00 00 B3= 01 B3=G3 B2= 01 11 11 10 10 G1, G0 B2= G3 G2 + G3 G2 G3, G2 00 01 11 10 = G3 + G2 00 B1= G3 G2 G1 + G3 G2 G1 + G3 G2 G1 + G3 G2 G1 B1= 01 = (G3 G2 + G3 G2) G1 + (G3 G2 + G3 G2) G1 11 = (G3 + G2) G1 + (G3 + G2) G1 10 = (G3 + G2) (G1 + G1) = G3 + G2 + G1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  • 7. G3 B3 G2 B2 G1 B1 G0 B0