# 4 input And gate CMOS

Discussion in 'Homework Help' started by jstrike21, Feb 10, 2010.

1. ### jstrike21 Thread Starter Member

Sep 24, 2009
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This question compares two different ways to implement a four-input CMOS AND gate.
(a) A four-input AND gate can be constructed by three two-input CMOS AND gates. The outputs of two two-input AND gates are connected to the inputs of the third two-input AND gate. Draw the corresponding circuit diagram. How many transistors (both PMOS and NMOS) are required?
(b) Show how you can use only 2-input CMOS NAND and NOR gates to build the four-input AND gate. How many transistors (both PMOS and NMOS) are required? (Hint: Use DeMorgan's theorem.)

I have completed part A.
Im having trouble visualizing how I can do B

2. ### jstrike21 Thread Starter Member

Sep 24, 2009
104
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wouldnt this way be worse? I would think it would use the inverse of 3 nand gates. I dont know why they mention nor gates

3. ### jstrike21 Thread Starter Member

Sep 24, 2009
104
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anyone have any ideas?

4. ### Ron H AAC Fanatic!

Apr 14, 2005
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By DeMorgan's theorem:

$\overline{\overline{A \cdot B} +\overline{C \cdot D}}=A \cdot B \cdot C \cdot D$

It's definitely cheaper (by transistor count) than 3 AND gates.

5. ### jstrike21 Thread Starter Member

Sep 24, 2009
104
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thanks that really helped me out

6. ### Ron H AAC Fanatic!

Apr 14, 2005
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So tell us how many transistors it requires, and how many you saved compared to the 3 AND gates.

7. ### jstrike21 Thread Starter Member

Sep 24, 2009
104
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6 pmos and 6 nmos for a total of 12 for the nand nor circuit
9 pmos and 9 nmos for a total of 18 for the and circuit

8. ### Ron H AAC Fanatic!

Apr 14, 2005
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Excellent! For extra credit, can you do it with 10 transistors?

Sep 24, 2009
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10. ### Ron H AAC Fanatic!

Apr 14, 2005
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It's simple. If you can design a 2 input NAND, you can design a 4 input NAND. Then you just need an inverter to make in an AND gate.

11. ### dor Well-Known Member

Feb 20, 2009
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something like this

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12. ### Ron H AAC Fanatic!

Apr 14, 2005
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Yep. Very much like that.