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Comparators

Comparators. Combinational Design. Comparators. Equality and Magnitude Comparators TTL Comparators Comparator Networks Cascading 1-bit Comparators. Equality Comparator. XNOR. X Y Z 0 0 1 0 1 0 1 0 0 1 1 1. X. Z. Y. Z = !(X $ Y). 4-Bit Equality Comparator.

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Comparators

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  1. Comparators Combinational Design

  2. Comparators • Equality and Magnitude Comparators • TTL Comparators • Comparator Networks • Cascading 1-bit Comparators

  3. Equality Comparator XNOR X Y Z 0 0 1 0 1 0 1 0 0 1 1 1 X Z Y Z = !(X $ Y)

  4. 4-Bit Equality Comparator FIELD A = [A0..3]; FIELD B = [B0..3]; FIELD C = [C0..3];

  5. 4-bit Equality Detector A[3..0] Equality Detector A_EQ_B B[3..0]

  6. 4-bit Magnitude Comparator A_LT_B A[3..0] Magnitude Detector A_EQ_B B[3..0] A_GT_B

  7. Magnitude Comparator How can we find A_GT_B? How many rows would a truth table have? 28 = 256!

  8. Magnitude Comparator Find A_GT_B Because A3 > B3 i.e. A3 & !B3 = 1 If A = 1001 and B = 0111 is A > B? Why? Therefore, one term in the logic equation for A_GT_B is A3 & !B3

  9. Magnitude Comparator A_GT_B = A3 & !B3 + ….. Because A3 = B3 and A2 > B2 i.e. C3 = 1 and A2 & !B2 = 1 If A = 1101 and B = 1011 is A > B? Why? Therefore, the next term in the logic equation for A_GT_B is C3 & A2 & !B2

  10. Magnitude Comparator A_GT_B = A3 & !B3 + C3 & A2 & !B2 + ….. Because A3 = B3 and A2 = B2 and A1 > B1 i.e. C3 = 1 and C2 = 1 and A1 & !B1 = 1 If A = 1010 and B = 1001 is A > B? Why? Therefore, the next term in the logic equation for A_GT_B is C3 & C2 & A1 & !B1

  11. Magnitude Comparator A_GT_B = A3 & !B3 + C3 & A2 & !B2 + C3 & C2 & A1 & !B1 + ….. Because A3 = B3 and A2 = B2 and A1 = B1 and A0 > B0 i.e. C3 = 1 and C2 = 1 and C1 = 1 and A0 & !B0 = 1 If A = 1011 and B = 1010 is A > B? Why? Therefore, the last term in the logic equation for A_GT_B is C3 & C2 & C1 & A0 & !B0

  12. Magnitude Comparator A_GT_B = A3 & !B3 + C3 & A2 & !B2 + C3 & C2 & A1 & !B1 + C3 & C2 & C1 & A0 & !B0

  13. Magnitude Comparator Find A_LT_B A_LT_B = !A3 & B3 + C3 & !A2 & B2 + C3 & C2 & !A1 & B1 + C3 & C2 & C1 & !A0 & B0

  14. Comparators • Equality and Magnitude Comparators • TTL Comparators • Comparator Networks • Cascading 1-bit Comparators

  15. 1 20 P>Q Vcc 1 16 2 19 B3 Vcc P0 P=Q 2 15 3 18 A<Bin A3 Q0 Q7 3 14 4 17 B2 A=Bin P1 P7 4 13 5 16 A>Bin A2 Q1 Q6 5 12 6 15 A1 A>Bout P2 P6 6 11 7 14 A=Bout B1 Q2 Q5 7 10 8 13 A<Bout A0 P3 P5 8 9 9 12 GND B0 Q3 Q4 10 11 GND P4 74LS85 74LS682 TTL Comparators

  16. Cascading two 74LS85s

  17. Comparators • Equality and Magnitude Comparators • TTL Comparators • Comparator Networks • Cascading 1-bit Comparators

  18. 1-Bit Magnitude Comparator

  19. 4-Bit Magnitude Comparator X Y 1101 0110 1110 1011 1011 1011 0101 0111 1010 1011 gt = 1 eq = 1 lt = 1

  20. Tree comparator network

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