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Comparators Combinational Design

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**Comparators Equality and Magnitude Comparators TTL Comparators**

Comparator Networks Cascading 1-bit Comparators

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**Equality Comparator XNOR X Y Z 0 0 1 0 1 0 X 1 0 0 Z 1 1 1 Y**

X Z Y Z = !(X $ Y)

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**4-Bit Equality Comparator**

FIELD A = [A0..3]; FIELD B = [B0..3]; FIELD C = [C0..3];

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**4-bit Equality Detector**

A_EQ_B B[3..0]

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**4-bit Magnitude Comparator**

A_LT_B A[3..0] Magnitude Detector A_EQ_B B[3..0] A_GT_B

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**Magnitude Comparator How can we find A_GT_B?**

How many rows would a truth table have? 28 = 256!

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**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

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**Magnitude Comparator A_GT_B = A3 & !B3 + ….. Because A3 = B3 and**

+ ….. 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

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**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

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**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

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**Magnitude Comparator A_GT_B = A3 & !B3 + C3 & A2 & !B2**

+ C3 & C2 & A1 & !B1 + C3 & C2 & C1 & A0 & !B0

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**Magnitude Comparator Find A_LT_B A_LT_B = !A3 & B3 + C3 & !A2 & B2**

+ C3 & C2 & !A1 & B1 + C3 & C2 & C1 & !A0 & B0

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**Comparators Equality and Magnitude Comparators TTL Comparators**

Comparator Networks Cascading 1-bit Comparators

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

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Cascading two 74LS85s

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**Comparators Equality and Magnitude Comparators TTL Comparators**

Comparator Networks Cascading 1-bit Comparators

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**1-Bit Magnitude Comparator**

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**4-Bit Magnitude Comparator**

X Y gt = 1 eq = 1 lt = 1

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**Tree comparator network**

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