# Design of a 4-bit comparator

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1 Concordia University Project Report for COEN6511: ASIC Design Instructor: Dr. A.J.AL-Khalili Design of a 4-bit comparator Xin Dong ID: Minghai Peng ID: Department of Electrical and Computer Engineering Concordia University Montreal, Quebec

2 Abstract 2 1 Introduction Description of the project Performance Measures Simulation Layout Design Kit and process technology Logic design for 4-bit comparator logic design procedure Bit Comparator Bit Comparator Implement Logic simulation.9 3 Schematic level design and simulation XNOR circuit and simulation NOR circuit and simulation SS1 circuit and simulation SS2 (4 Input AND) circuit and simulation Bit comparator circuit and simulation Layout and test Layout of XNOR Layout of NOR Layout of SS Layout of SS Layout of 4-Bit Comparator Conclusion 30 5 Package 31 6 Summary.34 7 Reference.35 1

3 ABSTRACT The goal of this project for the course COEN 6511 is to design a 4-bit comparator, aiming to master the techniques of ASIC design. The details of designing a 4-bit comparator are given in this report. It involves the methodology, circuit implementation, schematic simulation, layout and packaging. We start from logic gate level, go up to the circuit level and then draw the layout in the environment of CMOSIS5 in which the minimum drawing layout size is 0.6μ. Finally we extract the layout as a symbol in the schematic for re-simulation to obtain the results of the performance measure. In designing, propagation delay, Area (A) and power are considered. All parameters of circuit are decided and the circuit plot and waveform are produced, and we would test and verify every part of the CMOS circuit developed by Cadence development tools. The test results from simulation can meet the requirement. It means that the logic design, schematic and layout are correct, and our project can satisfy the requirements. 2

4 1. Introduction 1.1 Description of the project The goal is the design of a 4-bit comparator. Input two 4-bit numbers A & B. Output is 3-bit (A<B, A>B and A=B). We may use any comparison form and any logic form static, dynamic, or any variation of these or within these families. 1.2 Performance Measures: (1) Area (A), Time (T), Power (P), or AT 2 are used as circuit performance. Initially we are allowed to specify anyone of these factors to optimize our design. (2) Testing: Choose an optimum test vector to test the design. (3) Noise Margins: we are free to choose logic swing. The noise margins should be at least 10% of the voltage swing. (4) Rise and Fall times: All input signals and clocks have rise and fall times of less than 500 psec. The rise and fall times of the output signals (10% to 90%) should not exceed 1.5 nsec. (5)Load capacitance: Each output bit of the comparator should have a 20 ff load. 1.3 Simulation: Perform logic simulation, Circuit Simulation, and re-simulate the extracted circuit after circuit extraction. 1.4 Layout: Layout two gates of your design fully. Perform DRC. Extract the design and simulate it again and characterize these gates. We are allowed to use any library cell from CADENCE. We are to perform DRC on the final design, extract it and simulate it again to obtain performance measures. Then we are to place and route the complete chip including all I/O drivers and PADs. Give a complete specification for the circuit. 1.5 Design Kit and process technology We develop our project by using the Schematic Editor and the Analog Artist simulation tools available from Cadence package (CMOSIS5 design kit). The CMOSIS5 design kit is based on the Hewlett-Packard CMOS14TB process. This is a high-speed, high-density 0.5 micron CMOS process that features a 0.6 micron drawn gate length optimized for 3.3 V operation. 3

5 2 Logic design for 4-bit comparator 2.1 logic design procedure Magnitude comparator is a combinational circuit that compares to numbers and determines their relative magnitude. A comparator is shown as figure 2.1. The output of comparator is usually 3 binary variables indicating: A>B A=B A<B Figure bit comparator For a 2-bit comparator (Figure 2.2), we have four inputs A1A0 and B1B0 and three outputs: E (is 1 if two numbers are equal) G (is 1 when A > B) and L (is 1 when A < B) Figure bit comparator If we use truth table and KMAP, the result is E= A 1A 0B 1B 0 + A 1A0B 1B0 + A1A0B1B0 + A1A 0B1B 0 or E=(( A0 B0) + ( A1 B1)) G = A1B 1 + A0B 1B 0 + A1A0B 0 L= A 1B1 + A 1A 0B0 + A 0B1B0 Here we use simpler method to find E (called X) and G (called Y) and L (called Z) (1) A=B if all Ai= Bi 4

6 It means X0 = A0B0 + A 0B 0 and X1= A1B1 + A 1B 1 Table 2.1 Ai Bi Xi If X0=1 and X1=1 then A0=B0 and A1=B1 Thus, if A=B then X0X1 = 1 it means X= (A0B0 + A 0B 0)(A1B1 + A 1B 1) since (x y) = (xy +x y ) X= ( A0 B0) ( A1 B1) = (( A0 B0) + ( A1 B1)) It means for X we can NOR the result of two exclusive-or gates. (2) A>B means Table 2.2 A1 B1 Y If A1=B1 (X1=1) then A0 should be 1 and B0 should be 0 Table 2.3 A0 B0 Y For A> B: A1 > B1 or A1 =B1 and A0 > B0 It means Y= A1B 1 + X1A0B 0 should be 1 for A> B. (3)For B>A: B1 > A1 or A1=B1 and B0> A0 Z= A 1B1 + X1A 0B0 5

7 2.2 4-Bit Comparator The procedure for binary numbers with more than 2 bits can also be found in the similar way. The figure 2.3 shows the 4-bit magnitude comparator. Input A=A3A2A1A0; B=B3B2B1B0 A3 x3 B3 A2 x2 B2 (A<B) A1 x1 B1 A0 x0 (A>B) B0 (A=B) 4-Bit Magnitude Comparator Figure bit Magnitude Comparator (1)A= B : A3=B3, A2=B2, A1=B1, A0=B0 xi = AiBi + Ai Bi XOR-Invert = (AiBi +Ai Bi) = (Ai +Bi)(Ai+Bi ) = Ai Ai + Ai Bi + AiBi + BiBi = AiBi + Ai Bi Output: x3x2x1x0 6

8 (2)A> B Output: A3B 3 + x3a2b 2 + x3x2a1b 1+ x3x2x1a0b 0 (3)(A< B) Output: A 3B3 + x3a 2B2 + x3x2a 1B1+ x3x2x1a 0B0 Table 2.4 Truth table of 4-Bit Comparator COMPARING INPUTS OUTPUT A3, B3 A2, B2 A1, B1 A0, B0 A > B A < B A = B A3 > B3 X X X H L L A3 < B3 X X X L H L A3 = B3 A2 >B2 X X H L L A3 = B3 A2 < B2 X X L H L A3 = B3 A2 = B2 A1 > B1 X H L L A3 = B3 A2 = B2 A1 < B1 X L H L A3 = B3 A2 = B2 A1 = B1 A0 > B0 H L L A3 = B3 A2 = B2 A1 = B1 A0 < B0 L H L A3 = B3 A2 = B2 A1 = B1 A0 = B0 H L L A3 = B3 A2 = B2 A1 = B1 A0 = B0 L H L A3 = B3 A2 = B2 A1 = B1 A0 = B0 L L H H = High Voltage Level, L = Low Voltage, Level, X = Don t Care Bit Comparator Implement In order to implement the above circuit with fewer gates, we modify the circuit that is shown in figure

9 Figure 2.4 Logic diagram for a 4-bit comparator In order to reduce the area, we can still decrease the number of gates. The logic of A<B can be decided by A>B and A=B, so we can simplify the above circuit as figure 8

10 input NOR is used here to realize the function of A<B. The area of 2-input NOR is much less than that of G11~G15. On the other hand, fewer gates means fewer power, so this modification can greatly reduce the power dissipation. Therefore, the logic optimization is completed. Figure 2.5 Optimized logic diagram for a 4_bit comparator Seeing from the above diagram, we can use 11 gates to implement the 4-Bit comparator beside the inverters. The kind of gates includes XOR, AND, NOR. 4 gates of XOR are the same. 5 gates of AND have different number of inputs, but the principle of layout is the same. So does the NOR gate. 2.4 Logic simulation In order to verify above design, we start to do logic simulation. The diagram is shown as figure 2.6 9

11 Figure 2.6 Logic simulation diagram 10

12 Figure 2.7 Logic simulation result From the simulation results (figure 2.7), we can get the conclusion that our logic analysis is strictly right and then we begin to develop schematic level design. 11

13 3. Schematic level design and simulation From the simplified logic diagram, we can see that the circuit include 4 XOR gates, 5 AND gates with inputs from 2 to 5, 4 inputs and 2 inputs NOR and 5 inverters. In designing, we select the time and the area as performance index for optimization. Although area is an advantage for pseudo-nmos, we will not adopt it after entirely thinking about t d, t phl, t plh, area, power dissipation and other performance parameters. The time performance that we consider in this project includes propagation delay, T r and T f. As shown in the simplified logic diagram, The SS1 block is more complicated than other parts of circuit, so we choose propagation as the first index. We initially choose the size Wp_eff=1.73Wn_eff. In other blocks we initially choose Wp_eff= 3Wn_eff to make Tr equal to T f. In the diagram(figure 2.5), we can see that a 4 input NOR is used in the circuit. As we know, NOR gates are costly. For the same performance, it results in increased area, power, delay, output load capacitance (due to an increase in drain diffusion capacitance) and increase in input capacitance presenting higher load to driver circuit. Normally we convert our circuit to NAND and avoid use of large fan in NOR. But in this project, we still choose 2 inputs NOR as for practice since its fan-in is only 2, and measure the performance to get the detailed data with which we can compare the characteristics. Here we display four parts of comparator schematic: XNOR, NOR, SS1, SS2, and measure it after simulation. 3.1 XNOR circuit and simulation XNOR schematic diagram is shown as figure

14 Figure 3.1 Schematic of XNOR In the circuit, Wp=5.4microns Wn= 1.8microns, L= 0.6microns, The simulation is done in the Synopsys simulation platform. The simulation waveform is shown as figure 3.2: Figure 3.2 XNOR simulation waveform 13

15 The test result is shown as table 3.1 table 3.1 T PLH T PHL T r T f Average power 106.7ps 113.5ps 179.3ps 107.0ps 3.755e-7w 3.2 NOR circuit and simulation 2 inputs NOR schematic diagram is shown as figure 3.3 Figure 3.3 Schematic of NOR For each transistor in the circuit, L= 0.6microns, Wp=9.6microns, Wn=1.6micron The simulation waveform is shown as figure 3.4: 14

16 Figure 3.4 NOR simulation waveform The test result is shown as table 3.2 table 3.2 T PLH T PHL T r T f Average power 72.3ps 57.01ps 115.0ps 26.5ps 1.636e-8w 3.3 SS1 circuit and simulation The part of SS1 circuit includes G6,G7,G8,G9,G10 shown in the diagram. Its schematic diagram is shown as figure 3.5: 15

17 Figure 3.5 Schematic of SS1 In the circuit,wp= 10.8microns, Wn=3.6microns, L= 0.6micron The simulation waveform is shown as figure 3.6: 16

18 Figure 3.6 SS1 simulation waveform The test result is shown as table 3.3 table 3.3 T PLH T PHL T r T f Average power 689.4ps 257.6ps ps 716.0ps 1.744e-5w 3.4 SS2 (4 Input AND) circuit and simulation The schematic diagram of SS2 is shown as figure

19 Figure 3.7 Schematic of SS2 In the circuit, Wp=3.6microns, Wn=2.7micron, L=0.6micron The simulation waveform is shown as figure 3.8: Figure 3.8 SS2 simulation waveform 18

20 The test result is shown as table 3.4 Table 3.4 T PLH T PHL T r T f Average power 106.9p 111.0p 156.9p 146.2p 1.606e-07w Bit comparator circuit and simulation As we finished the above gates and circuit, we can integrate them as the whole 4-Bit comparator. The following (figure 3.9) is the testbench schematic of 4-Bit comparator. Figure 3.9 Testbench schematic of whole 4-bit comparator The simulation waveform is shown as figure

21 Figure bit comparator simulation waveform The test result is shown as table 3.5: Table 3.5 T PLH T PHL T r T f Average power ps ps 349.5ps 340.5ps 2.447e-06w As shown in the waveform and table, our design can meet the project requirements, and then we can start to develop the layout. 20

22 4 Layout and test Having finished the schematic level design and simulation successfully, we can do the layout and extract it to the schematic for test. Although we only need to layout 2 gates in this project and can use any standard library, we plan to layout all the gates by ourselves. The first reason is that the standard library maybe cannot meet our requirement. In most situations, we need to adjust the parameter of the transistor to meet the requirements of the project. For example, we need to adjust the Wp/Wn, Spacing, width to obtain the desired characteristics. However, the layout from standard library is difficult to adjust to meet our requirements. In addition, more layouts by hand can help us to improve the skills, and it is one of the purposes of the project we believe. 4.1 Layout of XNOR The layout of XNOR is shown as figure 4.1 Figure 4.1 the layout of XNOR We extract it as a symbol and test it in the test schematic. The simulation waveform is shown as figure 4.2: 21

23 Figure 4.2 Extracted XNOR simulation waveform The test result is shown as table 4.1 Table 4.1 T PLH T PHL T r T f NM L NM H Aaverage power Area (um 2 ) 230.0ps 305.2ps 349.6ps 271.1ps 0.93v 1.80v 1.812e-06w 19.8* Layout of NOR The layout of AND is shown as figure

24 Figure 4.3 the layout of NOR We extract it as a symbol and test it in the test schematic. The simulation waveform is shown as figure 4.4: Figure 4.4 Extracted NOR simulation waveform 23

25 The test result is shown as table 4.2: Table 4.2 T PLH T PHL T r T f NM L NM H Average power Area (um 2 ) 103.4ps 80.63ps 166.3ps 96.6ps 0.82v 1.76v 1.14e-06w 47.7* Layout of SS1 SS1 is the most complicated part in the project. Euler network of SS1 is shown as below according which we can minimize the area of layout. A3 B3 A1 B1 B2 A2 A3 B3 B3 A3 B3 A2 B2 A2 B2 A3 B3 A2 A3 B3 A1 A1 A2 B2 B1 A3 B3 A3 A2 A1 B0 A3 B3 A2 B2 A0 A0 A1 B1 Figure 4.5 Euler network of SS1 The layout of SS1 is shown as figure 4.6: 24

26 Figure 4.6 the layout of SS1 We extract it as a symbol and test it in the test schematic. The simulation waveform is shown as figure 4.7: 25

27 Figure 4.7 Extracted SS1 simulation waveform The test result is shown as table 4.3: Table 4.3 T PLH T PHL T r T f NM L NM H Average power Area (um 2 ) 712.4ps 593.8ps ps ps 0.98v 1.86v 4.3e-06w 47.7* Layout of SS2 The layout of SS2 is shown as figure 4.8: 26

28 Figure 4.8 the layout of SS1 We extract it as a symbol and test it in the test schematic. The simulation waveform is shown as figure 4.9: 27

29 Figure 4.9 Extracted SS2 simulation waveform The test result is shown as table 4.4: Table 4.4 T PLH T PHL T r T f NM L NM H average power Area (um 2 ) 212.3ps 195.2ps 265.5ps 164.6ps 0.85v 1.70v 1.77e-06w 16.5* Layout of 4-Bit Comparator The layout of 4-Bit comparator is shown as figure 4.10: 28

30 Figure 4.10 the layout of whole 4-bit comparator We extract it as a symbol and test it in the test schematic. The simulation waveform is shown as figure 4.9: 29

31 Figure 4.9 Extracted 4-bit comparator simulation waveform According to diagram above, the objective test results can be shown as table 4.5: Table4.5 T PLH T PHL T r T f NM L NM H Average power Area (um 2 ) ps ps 314.3ps 363.1ps 0.88v 1.82v 7.842e-06w 114.8* Conclusion From the layouts and tables, we can see that our design can satisfy the requirements. Area is a very important index in ASIC design. As for us, it is first time to layout gates and whole circuit. One of the experiences is that the minimum area of each gate does not mean the minimum area of whole circuit can be reached. For integration of gates, we also need to consider the direction of signal and its connection. Unreasonable layout of signal direction will waste much area when we integrate gates to a whole layout. 30

32 5 Packaging In our chip, there are 8 input pads : A0-A3,B0-B3. We use the pads of PADINC in hells library, then make the connection with the correspondent input in the circuit using metal1 dg layer. There are 3 output pads: G(A>B), E(A=B), L(A<B); The other two pads is VDD and VSS. The PAD connections are shown as figure 5.1: Figure 5.1 PAD connection Figure 5.2 is the whole circuit layout with I/O drivers. 31

33 Figure 5.2 the whole circuit layout The Pins are defined as figure 5.3 and table 5.1 Figure 5.3 Pins define 32

34 Pin Number Table 5.1 Signal Input Output VDD VSS(GND) 1 A0 2 B0 3 A1 4 B1 5 A2 6 B2 7 VSS 8 A3 9 B3 10 IDLE 11 L 12 E 13 G 14 VDD 33

35 6 Summary From the logic design, schematic level design and simulation, layout, re-simulation and packaging, it is clear that the logic design is correct and simple to implement. According to the basic principles of CMOS circuit design, the appropriate parameters can be decided after several attempts to get better performance during the course of the circuit schematic design. Guided by the schematic design and CMOSIS5 design Rules, the layout can be obtained after the rational arrangement of all parts of circuit. And re-simulating the extracted circuit after layout extraction, we attained the values of td, tplh, tphl, area, power dissipation and other performance parameters closer to the real application. The difference between the results from circuit design simulation and layout simulation provides us specific clues for improving the layout and at the same time, we must see that the layout is closer to real IC. For the practical application, some effects will be unavoidable, which is different from the circuit design simulation. Ordinarily, the time performance parameters from layout simulation are always greater than those from circuit design simulation. Another experience for layout is that the locally reasonable arrangement is not equal to the wholly reasonable arrangement and the wholly reasonable arrangement will be more significant for the design of large-scaled IC design. In general, we have learned many CMOS digital integrated circuits analysis methods and design techniques. We sincerely express our appreciation for our respectful tutor Dr. A.J.AL-Khalili. 34

36 7 References [1] Dr. Asim J. Al-Khalili, COEN 6511 Lecture notes [2] Cadence tutorial from website: [3] CMOS Digital Integrated Circuits Analysis and Design 3 rd Edition By Sung-Mo Kang and Yusuf Leblebici [4] Application-Specific Integrated Circuits By Michael John Sebastian Smith 35

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