EE101Lecture9

EE101Lecture9 - Mark Redekopp, All rights reserved...

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Unformatted text preview: Mark Redekopp, All rights reserved Introduction to Digital Logic Lecture 9: Gray Code Karnaugh Maps Mark Redekopp, All rights reserved Gray Code Different than normal binary ordering Reflective code When you add the (n+1) th bit, reflect all the previous n-bit combinations Consecutive code words differ by only 1-bit 1 1 1 1 when you move to the next bit, reflect the previous combinations 2-bit Gray code differ by only 1-bit Mark Redekopp, All rights reserved Gray Code Different than normal binary ordering Reflective code When you add the (n+1) th bit, reflect all the previous n-bit combinations Consecutive code words differ by only 1-bit 1 1 1 1 when you move to the next bit, reflect the previous combinations 2-bit Gray code 1 1 1 1 1 1 1 1 1 1 1 1 3-bit Gray code differ by only 1-bit differ by only 1-bit differ by only 1-bit Mark Redekopp, All rights reserved Karnaugh Maps 1 1 1 1 1 1 1 1 1 1 1 WX YZ 00 01 11 10 00 01 11 10 1 3 2 4 5 7 6 12 13 14 15 8 9 11 10 1 1 1 1 XY Z 00 01 11 10 1 1 2 3 6 7 4 5 3 Variable Karnaugh Map 4 Variable Karnaugh Map Every square represents 1 input combination Must label axes in Gray code order Fill in squares with given function values F= XYZ (1,4,5,6) G= WXYZ (1,2,3,5,6,7,9,10,11,14,15) Mark Redekopp, All rights reserved Karnaugh Maps W X Y Z F 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 WX YZ 00 01 11 10 00 01 11 10 1 3 2 4 5 7 6 12 13 14 15 8 9 11 10 Mark Redekopp, All rights reserved Karnaugh Maps 1 1 1 1 1 1 1 1 1 1 1 WX YZ 00 01 11 10 00 01 11 10 1 3 2 4 5 7 6 12 13 14 15 8 9 11 10 We can derive minterms from squares with 1 in them We can derive maxterms from squares with 0 in them Maxterm: w + x + y + z Maxterm: w + x + y + z Minterm: wxyz Minterm: wxyz Mark Redekopp, All rights reserved Karnaugh Maps WX YZ 00 01 11 10 00 01 11 10 1 3 2 4 5 7 6 12 13 14 15 8 9 11 10 XY Z 00 01 11 10 1 1 2 3 6 7 4 5 3 Variable Karnaugh Map 4 Variable Karnaugh Map Adjacent squares differ by 1-variable This will allow us to use T10 = AB + AB= A or T10 = (A+B)(A+B) = A Difference in X: 010 & 110 Difference in Z: 010 & 011 Difference in Y: 010 & 000 1 = 0 01 4 = 010 5 = 0101 7 = 01 1 1 13 = 1 101 Adjacent squares differ by 1-bit 0 = 0 2 = 010 3 = 01 1 6 = 1 10 Adjacent squares differ by 1-bit xyz + xyz = yz xyz + xyz = xy xyz + xyz = xz Mark Redekopp, All rights reserved...
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EE101Lecture9 - Mark Redekopp, All rights reserved...

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