Design of High Performance Magnitude Comparator

Design of High Performance Magnitude Comparator

1Kailash Chandra Rout, 2Sushmita Rath, 3Belal Ali

1Asst. Prof, Department of ECE 2Student, Department of ECE 3Student, Department of ECE

Gandhi Institute For Technology, Bhubaneswar, 752054

Abstract- A single-cycle tree-based binary comparator is realized in a 90-nm, 1.2-V CMOS process is presented in this paper. This novel comparator architecture is specifically designed for faster operation. This brief presents a detailed performance and power analysis of various state-of-the-art comparator designs across two CMOS technologies. At 90-nm technology, with a speed of 43.5ps and 180-nm technology, with a speed of 217.5ps, the proposed design demonstrates 56.936µw and 329µw power, respectively. In addition, the proposed work is 43.13% faster than existing design.

Index TermsBinary comparator, digital arithmetic.

I. INTRODUCTION

A binary comparator has always been an important block in an arithmetic logic unit and also has extensive applications in many digital systems, such as decoding of the x86 instructions. The recent emergence of multiple-input multiple output (MIMO) technology for next-generation communication systems has further aggravated the need for low-power high-performance comparators, because MIMO decoding algorithms require extensive iterations of binary number comparison.

Conventionally, a high-speed adder is the choice of design for high-performance binary comparison, at the cost of both power consumption and area. The heavy pipelining (3.5 clock cycles) requirement for ANT logic, however, made this design unsuitable for a single-cycle operation. A single-cycle, two-phase comparator that relies on priority encoders to decode the first unequal bit away from the most significant bit (MSB). A different priority-encoding (parallel-MSB-checking) algorithm along with a new priority encoder design and a MUX-based comparator structure is proposed in [4]. This implementation achieves superior delay performance compared to previous works, at the expense of both power dissipation and increase in the number of transistors.

All of the aforementioned works achieve high- performance operations using dynamic logic. While dynamic logic has demonstrated superior performance, as compared with static logic, it is not suitable for low-power operation because its data activity factor is always 0.5. On the other hand, static logic has an empirical of close to 0.1, making it advantageous in terms of power

consumption. In addition, a higher stack height is also less attractive in a deep sub micrometer process, where the VDD/Vt ratio is lower compared with an earlier technology, because transistors will exit the saturation mode sooner and be forced to operate in the linear region. Recently, tree-based comparators are proposed, where a tree structure, similar to the carry-merge tree of a parallel- prefix adder, is used to facilitate the comparison process. A tree-based comparator is theoretically one of the fastest schemes since the delay to compare two-bit numbers only depends on the logarithm of N. This tree structure comparator with a pre-encoding scheme to achieve a maximum stack height of two is proposed.

EXISTING COMPARATOR DESIGN

A brief description of the design principles of existing comparators is provided here.

A binary comparator compares two numbers and produces an output if one number is greater than, less than or equal to other number. If A and B are two numbers then the expression for different format can be derived using the truth table given Table 1.

For this designing, the Domino CMOS logic is used. In domino CMOS logic only non- inverting structures can be implemented using domino CMOS. Also charge sharing between the dynamic stage output node and the intermediate nodes of NMOS logic block may cause erroneous output. Fig. below shows a schematic diagram for 2-bit comparator

Table 1: Truth Table for comparison of two numbers

From Table,

Bbig=B.A Bless=A.B EQ=AB

2

A

2-bit Comparator

A>B A=B

CLK

a1

Vdd

a1

(a1 b1) . (a0 b0)

2

B

Fig 1: Block Diagram for binary Comparator

A<B

b1 b1

a0 a0

Lets consider two bits

A=a1, a0 B=b1, b0

And these two bits A and B comparison can be realized with

Bbig= a1. b1+ (a1b1). a0. b0 .(1)

Equal= (a1 b1). (a0 b0)…(2)

Fig 2(a) and (b) below shows the schematic diagram of 2-bit comparator.

Vdd

b0 b0

Fig 2(b): Schematic diagram for Existing Comparator (EQ)

TREE BASED COMPARATOR

CLK

a1 a1

a1.b1 + (a1 b1). a0 .b0

a1

A tree-based comparator that utilizes dynamic Manchester adders to reduce the number of critical stages to two. A static implementation of this design inevitably incurs performance and area penalties. For instance, a static Manchester adder requires an additional delete signal and has a tall PMOS transistor stack.

The proposed high-performance tree-based comparator

b1 b1 b1

a0 b0

is inspired by the fact that G (generate) and P (propagate) signals can be defined for binary comparisons, similar to the G and P signals for binary additions. Hence, the following key observation is made: A binary comparator is essentially a subset of the carry-merge tree in a parallel- prefix adder, where only the final carryout signal is necessary to interpret the result.

Fig 2(a): Schematic diagram for Existing Comparator (Bbig)

A, B [0]

0th Stage 1st Stage 2nd Stage Pre-encoder

Fig. below shows the circuit diagram of different stages of tree structure.

Vdd

A, B [1]

A, B [2]

A, B [3]

Pre-encoder

Pre-encoder

Pre-encoder

Bbig[3:0]

EQ[3:0]

CLK

a b

a.b

Fig3(a): Block diagram Representation of 4-bit Comparator

Lets consider 4-bit binary numbers (A3A0)& (B3B0) Then

Bbig[3:0]=A3. B3+(A3B3). A2.B2

+(A3B3).(A2B2).A1. B1

+(A3B3).(A2B2).(A1B1)A0.B0

(3)

EQ[3:0] =(A3B3). (A2B2). (A1B1).

(A0B0) (4)

Equation (3) may not be suitable for high performance operation when implementing with static logic, due to the tall transistor stack height and a complicated XNOR gate. An encoding scheme is employed to mitigate this problem.

The encoding equation is given as G[i]=A[i]. B[i]..(5)

EQ[i]=(A[i] B[i])(6)

Where i=03.The radix-2 comparison in equation (3) and

1. can be then simplified to

   Bbig[2j+1:2j] = G[2j+1]+ EQ[2j+1]. G[2j]…(7)

   EQ[2j+1:2j] = EQ[2j+1] . EQ[2j]…(8)

   Where j=01, G[i] signal is used for B[i]>A[i] and EQ[i] signal is used for A[i]=B[i].

   Bbig[3:0]=A3.B3+(A3B3). A2. B2

   +(A3B3).(A2B2). A1.B1

   +(A3B3).(A2B2).(A1B1).A0.B0

   =A3.B3+(A3B3)[A2.B2+(A2B2) [A1.B1+(A1B1).A0.B0]]

   =G3+EQ3 [G2+EQ2 [G1+EQ1.G0]]

   =Bbig[3:2]+EQ[3:2].Bbig[1:0]…….(9)

   Finally, Bbg and EQ in a N-bit comparator are computed using

   Bbig[N-1:0]=

   GN-1+ )

   (10)

   EQ[N-1:0]= …(11)

   CLK

   CLK

   Fig 3(b): Pre-encoder stage for Bbig

   Vdd

   a b

   1. a

   2. b

Fig 3(c): Pre-encoder stage for EQ

Vdd

G1+EQ1.G0

G1 EQ1

G0

Fig 3(d): Circuit diagram for stage 1(Bbig)

Vdd

Circuit Layout Implementation

CLK

EQ0

EQ1

Fig 3(e): Circuit diagram for Stage 1(EQ)

Vdd

EQO.EQ1

Fig 4(a): Design of Existing Comparator Architecture

CLK

G1

EQ1

G1+EQ1.G0

Fig 4(b): Design of Tree Comparator Architecture

Simulation of Comparator Architecture

G0

CLK

Fig 3(f): Circuit diagram for Stage 2(Bbig)

Vdd

EQ0

EQ1

Fig 3(g): Circuit diagram for Stage 2(EQ)

EQO.EQ1

Fig 5(a): Simulation of Existing Comparator Architecture

Fig 5(b): Simulation of Tree Comparator Architecture

All simulation runs are done at layout level in the MICROWIND 3.1 design environment using two different CMOS technologies at nominal supply voltage at 27 C.

SIMULATION & COMPARISION

After simulation of 65nm, 90nm and 180nm designs,

final results are obtained for delay and power consumption and are shown in Table 2-3-4 respectively. Simulations have been carried out at these three technologies in MICROWIND 3.1.

Table 2: Simulation data using 65nm Technology

Table 3: Simulation data using 90nm Technology

CONCLUSION

A single-cycle radix-2 tree-based comparator has been proposed in this work. This design is demonstrated for high-performance operations, as compared with existing architecture and gives an improved delay performance of 43.13% than the existing comparator architecture.

ACKNOWLEDGEMENT

We are thankful to the Dean and HOD, Department of Electronics & Communication Engineering for providing us necessary permission to carry out this work.

REFERENCES

1. S. M. Kang, Y. Leblebici, CMOS Digital Integrated Circuits: Analysis & Design, TATA McGraw- Hill Publication, 3e, 2003.

2. M. Mano, Digital Electronic Circuit, TATA McGraw- Hill Publication, 3e, 2003.

3. P. Chuang, M. Sachdev, D. Lii, A Low-Power High-Performance Single-Cycle Tree-Based 64-Bit Binary ComparatorIEEE Trans. Cir. & syst. II, vol.59, no.2, pp.489-493, Feb. 2012.

4. C.-H. Huang and J.-S. Wang, High-performance and power-efficient CMOS comparators, IEEE J. Solid-State Circuits, vol. 38, no. 2, pp. 254262, Feb. 2003

Table 4: Simulation data using 180nm Technology

Table 5: Comparison of speed