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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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Comparators Combinational Design. Comparators Equality and Magnitude Comparators –CSE 171 (Designed using CUPL) TTL Comparators Comparator Networks Cascading.

Comparators Combinational Design. Comparators Equality and Magnitude Comparators –CSE 171 (Designed using CUPL) TTL Comparators Comparator Networks Cascading.

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