Homework Assignment #1

EE 477 Spring 2011 Professor Parker

Hardcopies due in the course boxes on the first floor of EEB 5 PM 2/1/2011

Ecopies due 11:59 PM 2/1/2011 using the "Assignment" Function on DEN

To ensure academic privacy, please use a cover page on your homework hard copies that does not contain any work.

1. (5%) Give the Boolean expressions for a three-bit comparator computation with output C and inputs X_i, X_i+1, X_i+2 and Y_i, Y_i+1 and Y_i+2. X and Y are being compared. C is high (1) when X < Y, and 0 (zero) otherwise. The ith bit is the least significant bit.

2. (10%) Show an implementation of the comparator computation in Problem 1 above at the gate level using complementary NAND, NOR and INV gates. You may not use XOR or XNOR gates.

3. (15%) Show an implementation of the comparator computation from Problem 2 at the circuit (transistor) level. For an example of complementary CMOS NAND gates and inverter, See Fig. 1.

You only need to show each circuit level gate type once, and you can use a symbol for the others. A 3-input NAND gate is different from a 2-input NAND gate so you should show both circuits.

4. (10%) Show a compound gate implementation of the comparator at the circuit (transistor) level, similar to the compound gate shown in Fig. 2. You may need an additional inverter at the output of a compound gate to get correct results.

5. (10%) Show a stick diagram of a 5-input NOR gate, labeling the layers or using colors for the different layers as shown in lecture.

6. (10%) Use the same style of design as Problem 3 (See Fig. 1) but use only NAND and INVERT gates to build a transistor-level circuit that implements the output sum of a 1-bit adder, assuming there is a carry in (full adder). You may not use XOR or XNOR gates. You do not need to compute the carry-out.

Note: You can assume the complements of the inputs also to be inputs to the circuit. You can use gates with any number of inputs.

7. (10%) Again refer to the style of compound gate circuit used in lecture (See Fig. 2 for an example).

Redesign your circuit from Problem 6 at the transistor level using a compound gate. You might have to invert the output with an inverter. Show the compound gate transistor diagram. Compare the number of transistors to the original design in Problem 6.

8. (10%) Show a design at the transistor level of a 5-input mux using transmission gates.

9. (10%) Design a latch that can be synchronously set and reset. The MUX used in the latch should be constructed using NAND gates.

10. (5%) Make a directory (folder) on your UNIX account that is called HW1. Create a small file on your UNIX account that contains your full name on the first line and your student number on the second line. Use EMACS or any other unix editor to create the file. Save the file in the HW1 directory as yourlastname.txt. Change the directory to HW1. Give the results of typing the command ls -l yourlastn* , leaving off the last three letters of your last name. You can provide a print screen or just copy / paste the text. If your last name is two words with a space in between, use the last word.

11. (5%) What is the volume in cm³ of a box with width 8.7x10⁹ Å, length 2x10⁵um, and a thickness of 50 mm?