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Unformatted text preview: Lecture 6: Combinational Circuit Design From http://www3.hmc.edu/~harris/cmosvlsi/ 4e/index.html CMOS VLSI for Computer Engineering Outline • Bubble Pushing • Compound Gates • Logical Effort Example • Input Ordering • Asymmetric Gates • Skewed Gates • Best P/N ratio 10: Combinational Circuits 2 CMOS VLSI for Computer Engineering Example 1 module mux(input s, d0, d1, output y); assign y = s ? d1 : d0; endmodule 1) Sketch a design using AND, OR, and NOT gates. 10: Combinational Circuits 3 D0 S D1 S Y CMOS VLSI for Computer Engineering Example 2 2) Sketch a design using NAND, NOR, and NOT gates. Assume ~S is available. 10: Combinational Circuits 4 Y D0 S D1 S CMOS VLSI for Computer Engineering Bubble Pushing • Start with network of AND / OR gates • Convert to NAND / NOR + inverters • Push bubbles around to simplify logic Remember DeMorgan’s Law 10: Combinational Circuits 5 Y Y Y D Y (a) (b) (c) (d) CMOS VLSI for Computer Engineering Example 3 3) Sketch a design using one compound gate and one NOT gate. Assume ~S is available. 10: Combinational Circuits 6 Y D0 S D1 S CMOS VLSI for Computer Engineering Compound Gates • Logical Effort of compound gates 10: Combinational Circuits 7 A B C D Y A B C Y A B C C A B A B C D A C B D 2 2 1 4 4 4 2 2 2 2 4 4 4 4 g A = 6/3 g B = 6/3 g C = 5/3 p = 7/3 g A = 6/3 g B = 6/3 g C = 6/3 p = 12/3 g D = 6/3 Y A A Y g A = 3/3 p = 3/3 2 1 Y Y unit inverter AOI21 AOI22 A C D E Y B Y B C A D E A B C D E g A = 5/3 g B = 8/3 g C = 8/3 g D = 8/3 2 2 2 2 2 6 6 6 6 3 p = 16/3 g E = 8/3 Complex AOI Y A B C = + Y A B C D = + ( 29 Y A B C D E = + + Y A = CMOS VLSI for Computer Engineering Example 4 • The multiplexer has a maximum input capacitance of 16 units on each input. It must drive a load of 160 units. Estimate the delay of the two designs. 2 2 4 (4 / 3) (4 / 3) 16 / 9 160/ 9 ˆ 4.2 ˆ 12.4 N P G F GBH f F D Nf P τ = + = = = = = = = = + = g 4 1 5 (6/ 3) (1) 2 20 ˆ 4.5 ˆ 14 N P G F GBH f F D Nf P τ = + = = = = = = = = + = g 10: Combinational Circuits 8 Y D0 S D1 S Y D0 S D1 S H = 160 / 16 = 10 B = 1 N = 2 CMOS VLSI for Computer Engineering Example 5 • Annotate your designs with transistor sizes that achieve this delay. 6 6 6 6 10 10 Y 24 12 10 10 8 8 8 8 8 8 8 8 25 25 25 25 Y 16 16 160 * (4/3) / 4.2 = 50 160 * 1 / 4.5 = 36 10: Combinational Circuits 9 Y 8 8 8 8 8 8 8 8 25 25 25 25 Y 16 160 * (4/3) / 4.2 = 50 Y Y CMOS VLSI for Computer Engineering Input Order • Our parasitic delay model was too simple Calculate parasitic delay for Y falling • If A arrives latest? 2 τ • If B arrives latest? 2.33 τ 10: Combinational Circuits 10 6C 2C 2 2 2 2 B A x Y CMOS VLSI for Computer Engineering Inner & Outer Inputs • Inner input is closest to output (A) • Outer input is closest to rail (B) • If input arrival time is known Connect latest input to inner terminal 10: Combinational Circuits 11 2 2 2 2 A B Y CMOS VLSI for Computer Engineering Asymmetric Gates • Asymmetric gates favor one input over another...
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 Fall '11
 LukeTheogarajan
 Gate, Transistor, Logic gate, NMOS logic, logic families, CMOS VLSI

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