Asynchronous comparator design• Motivation• Background: Sync and Async comparators• Delay-insensitive carry-lookahead comparators• Complexity Analysis• Conclusions

Motivation

• Comparison is one of the most important

operations in digital systems.

• Comparators are used in ALUs, cache memory,

MMU and data hazard detection.

• Integer comparison: use an integer adder.

Problem: addition time > comparison time.

• High speed comparison is needed.

Background: Binary Comparison

• Worst case: A=B A: 01101110 B: 01101110

• Best case: A>B A: 01101110 B: 10101110

• Comparators can perform average case behavior

Background

• Ripple-Carry Comparator(Sync):

• Flow table specification:

Background

• Delay-Insensitive Ripple-Carry Comparator:

• Flow table:

Background

• Ripple-Carry Comparator:• Logic complexity: O(n)• Time complexity: O(n)

• Delay-Insensitive Ripple-Carry Comparator: • Logic complexity: O(n)• Time complexity: O(1)

Carry-Lookahead Comparators• RCC requires n stage-propagation delays.

• Use carry-lookahead comparators(CLC).

• CLCs:

Logic complexity: O(n) Time complexity: O(log n)

8-bit carry-lookahead comparator

DI Carry-Lookahead Comparator• Delay-Insensitive Carry-Lookahead Comparators may be implemented by using delay-insensitive code.

1. dual-rail signaling: input bits 2. one-hot code: internal signals, s, g, e (S, G, E). S: smaller (A<B) G: greater (A>B) E: equal (A=B)

CMOS Implementation

• DI P-module:

CMOS Implementation

• DI I-module:

CMOS Implementation

• DI SI-module: 3 2-input AND gates.

CMOS Implementation

• Speed-up circuits for S and G signals: Dynamic OR gates.

CMOS Implementation

• Speed-up circuits for E signals: Dynamic OR gate:

SPICE Simulation:

SPICE Simulation contains two parts:• Random number inputs: 10000 random generated input pairs• Statistical data: running examples on a 32-bit ARM emulator

SPICE Simulation:

• Random number inputs: 10000 random generated input pairs a. RCC: 32.4ns b. CLC: 6.2ns

SPICE Simulation:

• Confidence Limits:

SPICE Simulation:

• Confidence Limits:

SPICE Simulation:

• Distribution of typical-case comparisons:

SPICE Simulation:

• SPICE simulation results: dynamic traces

Conclusions

• A new pratical design of DI comparator.• Theoretically,

• Logic Complexity:((n)).• Time Complexity:((1)).

• Reality:• more than 2 times faster than its sync

counterpart with 80% usable clock.• Suitable for VLSI implementation.