1 DIGITAL ELECTRONICS

2 OVERVIEW –electronic circuits capable of carrying out logical (boolean) and arithmetic operations on information stored as binary numbers. –referred to as digital electronic circuits or logic circuits –Digital implies that the circuits are operating on numbers or digits, and "logic" implies that the circuits carry out logical or boolean operations.

3 OVERVIEW –information processed by digital electronic circuits is in the form of electrical, binary signals. –Signals are voltage levels, there are two possible values that they may have. –Most common systems use voltages of less than 1 volt to represent a 0 (False, Off), and voltages in the range of 3.5 to 5 volts to represent a 1 (True, On).

4 OVERVIEW integrated circuits - chips a number of circuits all on one device –small-scale integrated circuits (SSI), less than 100 components –medium-scale (MSI), up to a thousand components –large-scale (LSI), up to a hundred thousand components –very-large scale (VLSI), up to a million components –super-large scale (SLSI), more than a million components

5 LOGIC GATE OPERATION – Digital circuits that are used to carry out Boolean logic operations are referred to as gates. –They perform a set of three basic operations from which all the other circuits can be developed. –Gates are manufactured as chips with a number of gates of a particular type on a chip.

6 AND Gate –The AND gate is a gate whose output is a 1 only if all of it's inputs are 1's. In the case of a 2-input gate as illustrated, the output C is a 1 only if both A and B are 1's. –This is stated arithmetically as: C = A · B

7 Two Input AND Gate

8 –The truth table for the gate is:

9 THE OR GATE –The OR gate is a gate whose output is a one if any of it's inputs are one. In the case of a 2- input gate as illustrated, the output C will be a 1 if either A or B or both A and B are 1's. This is stated arithmetically as: C = A + B

10 OR Gate

11 –The truth table for the OR gate is:

12 THE INVERTER (NOT GATE) –The Inverter is a single input gate whose output is the inverse or opposite of it's input. arithmetically this is stated as: B = A

13 NOT Gate

14 –The truth table of the inverter is:

15 THE EXCLUSIVE OR GATE –The Exclusive OR gate is a gate whose output is a 1 if either of it's inputs is a one, but not if both of them are ones. Arithmetically this is stated as: C = A  B

16

17 –The truth table for the Exclusive OR gate:

18 NEGATIVE OUTPUT GATES There are two other major gates that are effectively created by adding an inverter to the outputs of the AND and OR gates.

19 THE NAND GATE –The NAND gate is a gate whose output is a 0 only if all of it's inputs are 1's. Arithmetically this is stated as: C = A · B

20 The NAND Gate

21 –The truth table for the NAND gate:

22 THE NOR GATE –The NOR gate is a gate whose output is a 0 if any of it's inputs are 1's. Arithmetically this is stated as: C = A + B

23 NOR Gate

24 –The truth table of the NOR gate:

25 DEMORGAN'S THEOREMS –Demorgan's theorems are very useful to us as we analyze and describe logic circuits. They simplify expressions in which the product or sum of variables is complemented.

26 DEMORGAN'S THEOREMS A. B = A + B

27 DEMORGAN'S THEOREMS A + B = A · B

28 Digital Adders Adders are a major function of a computer. –Found in the Central Processor Unit in the Arithmetic Logic area.

29 Half-Adder

30 Full Adder

31 Decoding Circuits Have to be able to decode particular combinations of signals. –Used to transfer data from or to memory or peripherals. –Need to decode the address lines to determine where the data is to go. –Take a number of input signals and provide enough outputs to indicate what the input was.

32 Decoding Circuits If the input is two binary signals, there would have to be four outputs. One output for each input combination.

33 Two Bit Decoder D1 D

34 Data Selector (Multiplexer) Combination of decoder and bus enable logic Used when a number of different signals have to be gated to a bus.

35 Data Selector

36 Data Selector

37 Data Selector Above circuit would have to be repeated 32 times for a 32-bit bus is example of choosing only one of two lines to be transferred with the circuit being duplicated four times on the same chip.

38 FLIP-FLOPS Basic logic circuit used to store binary information. Forms basis of circuits used to create timing and counting signals. Foundation for memory and a major component in processor registers.

39 FLIP-FLOPS F/F remember a binary value. Said to be “Set” when a 1 has been stored. Said to be “Cleared” when a 0 has been stored. Most often a signal, usually the computer clock signal, is used to tell F/F to store a value. Output from circuit is Q, sometimes its compliment is also present.

40 Clocked S-R Flip-Flop

41 D-TYPE FLIP-FLOP Simplified input. Does not allow F/F to be set and cleared at the same time. Needs a clock signal to be set or cleared.

42 D-TYPE FLIP-FLOP

43 D-TYPE FLIP-FLP PRE and CLR are used to set and clear the F/F without a clock signal. A ‘0’ on PRE would set F/F A ‘0’ on CLR would clear F/F

44 D-TYPE FLIP-FLOP

45 J-K FLIP-FLOP

46 J-K FLIP-FLOP Differs from D and S-R F/F in following ways: –Changes state on falling edge of clock signal. –Toggles when J and K are high. –J corresponds to S, K corresponds to R.

47 REGISTERS Used to store binary data. Similar to a memory location but normally in the processor. Consists of a number of F/F whose inputs represent the digits of a binary number. Data is loaded into all F/F of register simultaneously by a clock input.

48 REGISTERS

49 COUNTERS Used to count clock pulses at the clock inputs. How high the counter counts depends on the number of F/F in counter.

50 TWO-BIT COUNTER

51 TWO-BIT COUNTER