EET 252

1. EET 252 Digital Systems II Professor Nick Reeder

2. Reminders • Please turn off cell phones. • No food or soft drinks in the classroom. • Stow water bottles at floor level.

3. EET 252 Unit 1Review; Arithmetic Logic Units • Review Floyd, Chapter 2 and Chapters 6 to 9. • Study Unit 1 e-Lesson. • Do Lab #1. • Homework #1 and Lab #1 due next week. • Quiz next week.

4. Overview of This Week’s Lecture • Unused Inputs • Pull-up Resistors • Review of Logical Operations • Review of Arithmetic Operations • Arithmetic Logic Units

5. Unused Gate Inputs (Floyd, p. 143)

6. Tying Other Inputs HIGH or LOW • The same rules apply to other input pins (such as enable inputs). • To force them HIGH, tie them to VCCthrough a 1-kΩ resistor for TTL. • To force them LOW, tie them to ground.

7. But what about the Trainer’s Data Switches? • When you connect a TTL input pin to one of the trainer’s data switches and set the switch to HIGH, do you need a 1−kΩ resistor between the switch and the input pin?

8. From the Trainer’s Schematic Diagram

9. Don’t Tie Outputs HIGH or LOW • Remember that, in general, unused output pins should be left unconnected. Do not tie them HIGH or LOW.

10. Overview of This Week’s Lecture • Unused Inputs • Pull-up Resistors • Review of Logical Operations • Review of Arithmetic Operations • Arithmetic Logic Units

11. Pull-Up Resistor • A pull-up resistor is a resistor with one end connected to a HIGH voltage level and the other end connected to a point in a digital circuit. • The resistor’s purpose is to pull up the voltage at that point to a HIGH level when it would otherwise be in a float condition (not HIGH or LOW).

12. Pull-Up Resistor (Continued) • Three common uses of pull-up resistors: • On a switch connected to an input pin. • When interfacing two logic families that use different voltage levels. • On open-collector outputs (TTL) or open-drain outputs (CMOS).

13. First Use for Pull-Up Resistor: Switch on an Input Pin • Good explanation at http://www.seattlerobotics.org/encoder/mar97/basics.html • See also example on next slide from your textbook.

14. Figure 6.42 A simplified keyboard encoder. (Floyd, p. 316)

15. Second Use for Pull-Up Resistor: Interfacing Logic Families • Suppose we want to connect the output of a TTL gate to the input of a CMOS gate. • A TTL HIGH output may be as low as 2.4 V. • But CMOS expects at least 3.3 V for a HIGH. • Problem: The CMOS gate may interpret the TTL gate’s HIGH output as a LOW. • Solution? See next slide.

16. Figure 9–27 Using a pull-up resistor to interface TTL to CMOS.

17. Third Use for Pull-Up Resistor: Open Collector Outputs • As we’ll see next week, some TTL gates are intentionally designed with a missing transistor on the output. To work properly, such an output needs an external pull-up resistor. • One of the output pins on the chip in tonight’s lab is an open-collector output, and therefore needs a pull-up resistor.

18. Figure 14.31 TTL inverter with open-collector output.

19. Overview of This Week’s Lecture • Unused Inputs • Pull-up Resistors • Review of Logical Operations • Review of Arithmetic Operations • Arithmetic Logic Units

20. How Many Logical Operations? • You already know how to perform some logical operations on two input bits, A and B. Examples: • X = AB • X = A+B • Question: How many possible logical operations are there on two input bits?

21. How Many Logical Ops? (Continued) • Let’s list them all:

22. Overview of This Week’s Lecture • Unused Inputs • Pull-up Resistors • Review of Logical Operations • Review of Arithmetic Operations • Arithmetic Logic Units

23. Overview of This Week’s Lecture • Unused Inputs • Pull-up Resistors • Review of Logical Operations • Review of Arithmetic Operations • Arithmetic Logic Units

24. Arithmetic Logic Unit (ALU) • Central to any computer system is its ALU, which performs mathematical and logical operations on data. • In modern systems, the ALU is contained on the computer’s microprocessor chip. (See next slide, or Figure 13-3 on p. 724 of Floyd.) • In older systems, the ALU was a separate chip, such as the 74181.

25. Figure 13.3

26. 74181 ALU chip • Can perform 16 logical operations (bit-by-bit) and 16 arithmetic operations on two four-bit input numbers. • Data Sheet shows two truth tables: Table 1 if you’re considering data inputs & outputs to be active-low, and Table 2 if you’re considering data inputs & outputs to be active-high. • Data Sheet: 74LS181

27. Positive Logic versus Negative Logic • Any gate or logic circuit can be looked at from either an active-HIGH perspective (“positive logic”) or an active-LOW perspective (“negative logic”). • Example: The gates on a 7408 chip can be considered either positive-AND gates or negative-OR gates. • Data Sheet: 7408

28. 74181 ALU (Continued) • Caution: In the “Arithmetic Operations” columns of the 74181 truth tables, the + symbol always means logical OR, not addition. The word “PLUS” is used for addition.

29. 74181 ALU (Continued) • Fourteen Input Pins: • M is the mode pin (arithmetic or logic). • S0 to S3 select the operation performed. • Cn is the carry-in bit, used only during arithmetic ops (ignored during logic ops). • A0 to A3 form one of the 4-bit inputs. • B0 to B3 form the other 4-bit input.

30. 74181 ALU (Continued) • Eight Output Pins: • F0 to F3 form the 4-bit output. • Cn=4is carry-out bit, meaningful only for arithmetic ops. (Ignore it for logic ops.) • A=B is comparison bit, meaningful only when performing “A MINUS B” operation. (Ignore it for all other ops.) • P and G are carry-look-ahead bits for high-speed arithmetic, when 74181 is used in conjunction with 74182 chip. (We’ll ignore these.)