ECE 101 An Introduction to Information Technology Digital Logic

1. ECE 101An Introduction to Information TechnologyDigital Logic

2. Information Path Source of Information Digital Sensor Information Display Information Receiver and Processor Information Processor & Transmitter Transmission Medium

3. Combinational Logic Gates • Fundamental Gates • Exclusive OR • Seven Segment Displays • Binary Addition • Binary Subtraction • 2’s complement notation

4. Fundamental Logic Gates AND Gate Use a dot to indicate the AND operation A NAND = _ Y=A·B not AND = Y B NOT = _ A B Y=A·B Y 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 _ Y Y

5. Fundamental Logic Gates OR Gate Use a plus sign to indicate the OR operation NOR gate A _ Y=A+B = not OR = Y B _ A B Y=A+B Y 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 0 _ Y A B

6. Combinational Logic Gates • N input variables yields 2N possible inputs • A truth table lists output for all possible combinations of input variables • Combinational Logic Gates implement a truth table • Given a binary pattern b3 b2 b1 b0 • Implement with AND gate, so transform all given inputs into a set of 1’s since the union will give a one.

7. Combinational Logic Gates • Examples • Implement a circuit to produce a 6 • Implement a circuit to produce a 13 • More than one pattern, use Y = pattern 1 + pattern 2 + … pattern N • Implement a circuit to implement either a 6 or 14

8. Combinational Logic Gates • Fundamental Gates • Exclusive OR • Seven Segment Displays • Binary Addition • Binary Subtraction • 2’s complement notation

9. Seven segment displays

10. Truth Table to convert BCD codes to 7- segment display Logic circuit for the letter “a” to be displayed

11. Binary Adder Truth Table Binary Adder, Sum bit

12. Binary Subtraction • Subtracting a number is the same as adding the negative of the number 14-9=14+(-9)=5 • Use 2’s complement notation to get the negative number • First complement all the bits in the number • Then add one • 1310 = 011012 find –13 by 2’s complement: • Complement each bit 10010 • And add one: +00001 • To get 10011 the value of –13 • Add this now to 13 to get 00000

13. Sequential Logic Circuits • Depend upon past and present input values • Combinatorial: use truth tables • Sequential: use timing diagrams • Most common sequential logic circuits include “flip-flops”, each is capable of storing one bit of information. • “set-reset flip-flop”: basic computer memory cell • “toggle flip-flop”: basic computer counting cell

14. Set-Reset Flip-Flop • Computer’s basic memory cell • Implemented by two OR gates and two Not gates (or two NOR gates) that use feedback (connection of output to input). • Two inputs: S, set and R, reset and two outputs, Q and not Q • Note Q remembers whether S or R was “one” last – this is the memory capability of SRFF

15. S-R flip-flop

16. Addressable Memory • Uses both combinatorial and sequential logic • Random access memory (RAM) stores and retrieves binary data as needed • Each cell or memory location has a unique address • At the S input there is an AND gate with the address & input data • At the R input there is another AND gate with complement of the input data and the address

17. Addressable Memory • In order to be stored at a memory location the address signal must be 1 then the output of the memory (SRFF) is the DATA input value. • To retrieve the contents of the memory cell the out put is connected to an AND cell again with the address signal. • Hence the output of the AND occurs only when the address is 1

18. Toggle flip-flop

19. Toggle Flip-Flop • Basic computer counting cell • Two inputs, a toggle (T) and clear (C), and one output Q • The value of Q changes (or toggles) when when ever a 1 to 0 transition occurs at the input T • When a 1 appears at the C input, the Q resets to 0 and remains at 0 as long as C=1.

20. Binary Counting with T F-F Note the error here: “14” should be “13”.

21. Toggle Flip-Flop • As a result, Q has twice the period (or ½ the number of pulses) as T • By cascading a series of n, T-FF, and connecting to each output, a counter can be made up to 2n – 1.

22. Modulo-N Counter • A counter uses a chain of T-FFs • Recall M T-FFs count from 0 to 2M - 1 • Modulus (mod) of a counter is the number of counting states before it repeats itself • If we wish a counter that is not 0 to 2M – 1, then we must apply a clear (C) at some point to start the counting over again.

23. Modulo-6 Counter

24. Digital Clock • 7 segment display • Counts 60 Hz frequency of ac power line • Use of mod 60 to get to minutes from seconds • Use of mod 10 to get to 10 minute digits • Use of mod 6 to get to hours • Use of mod 12 to reset the clock