DIGITAL ELECTRONICS. Methods & diagrams : 1 Graph plotting : - Tables & analysis : - Questions & discussion : 6 Performance : 3

Transcription

1 DIGITAL ELECTRONICS Marking scheme : Methods & diagrams : 1 Graph plotting : - Tables & analysis : - Questions & discussion : 6 Performance : 3 Aim: This experiment will investigate the function of the basic AND, OR and NOT logic gates. These basic gates will be used to construct some simple digital electronic circuits and to investigate the function of these circuits in terms of their truth tables and their Boolean algebraic expressions. Preliminary Theory: Digital electronics uses only two voltage levels to encode and manipulate information. These levels are called logic 0 and logic 1 and are represented by the following voltages logic 0 = 0 V : LED off (dull) logic 1 = 5 V : LED on (bright) In the digital electronics kit provided, these levels can be detected by a red light of the emitting diode (LED) lights. All digital electronic circuits are made up from electronic logic devices called gates. The three basic gates are called AND, OR and NOT. The functions of these three gates are represented symbolically, and algebraically, in the table of the table below. A and B are the inputs to the gates and can be either logic 0 or logic 1 (that is, either 0 V or 5 V) and C is the gate output (again either 0 or 1). The algebra that is used to describe the function of individual gates, and the combination of these gates in circuits, is called Boolean algebra. Experimental Tasks: 1. Digital electronics kit The IEC digital electronics kit provided includes a power supply, diode resistor gates, integrated circuit (IC) gates, switches to supply logic levels and LEDs to indicate logic 28

2 levels. The general location of these different sections is shown in the diagram below. Other sections of the kit will not be used in this experiment. With the mains power to the transformer switched OFF, connect the 12 V output of the transformer to the 12 V input of the kit (labelled POWER INPUT ) and then switch on the mains power. Ensure that switches P1 and P2, located in the top left hand power supply section of the kit are switched to ON (i.e. to the right). Some of the LED indicators on the kit should be alight. If not, ask your demonstrator for assistance. Please note that you must NOT write on the logic boards (or any other equipment). Connect a voltmeter between any pin labelled 0 V and the output pin of one of the switches in the bottom right hand section of the kit. Be very careful not to bend these pins during the experiment. Record the voltage when the switch is on 0 and the voltage when it is on 1. These switches will be used to supply input logic levels to the inputs of gates. 2. Basic gates Select an AND gate from the IC GATES section of the kit. Connect a separate switch to supply logic levels to each of the two gate inputs. For all possible combinations of input levels, record the resulting output level as indicated by the LED on the output line. Record your results in a table like the one below. A table such as this is called a truth table and expresses the function of a logic circuit (in this case a single gate). 29

3 Describe the function of the gate (i.e. how the output is related to the inputs). Draw up a truth table for the OR gate and comment on the results. Draw up a truth table for the NOT gate and comment on the results. Check all your results using the diode resistor gates where the inputs are provided by dedicated switches. Using the printed circuit for the AND and OR diode resistor gates displayed on the bottom left hand corner of the kit as a guide, draw the circuit for these gates. Note that the black components that resemble are diodes, whose circuit symbol is and which only allow current to flow in the direction of the arrow. The other brown components are resistors. Explain how the AND and OR gates are implemented by the diode resistor circuit. 3. De Morgan s theorem An important theorem in the design of logic circuits is that due to De Morgan, namely (A + B) = A B For the left hand side of this equation, draw a logic circuit, wire it on the kit and measure its truth table. Repeat this procedure for the right hand side of the equation. Report on the confirmation of De Morgan s theorem by comparison of the two truth tables. De Morgan s theorems state the same equivalence in backward form: that inverting the output of any gate results in the same function as the opposite type of gate (AND vs. OR) with inverted inputs. So, an OR gate with all inputs inverted (NOR gate) behaves the same as a NAND (Negative-AND) gate, and an AND gate with all inputs inverted (NAND gate) behaves the same as a NOR (Negative-OR) gate. An OR gate can be wired up as such : (A + B) = (A B ). Write a boolean expression and draw the equivalent circuit for (A B) Wire it up as like before to confirm your answer. 30

4 4. Exclusive Or (XOR) gate As you have found, the OR gate output is logic 1 if either or both of the inputs are logic 1. In digital electronics an Exclusive Or (XOR) gate is also used where the output is logic 1 only if either input is 1, but NOT if both are 1. The truth table and symbol for XOR are shown in the following figure. A Boolean expression for XOR is A B = A B + A B Draw the logic circuit for the right hand side of the above equation using gate symbols. Wire this circuit on the kit and test its truth table. Compare your experimental results for the XOR truth table with that given above and comment on your success or otherwise. 5. Decoder An extremely important circuit in digital electronics is the decoder. Its block diagram is shown below, where I 1 and I 0 are the inputs and O 3, O 2, O 1 and O 0 are the outputs. The purpose of the decoder is to ensure that for each possible input code, only one of the outputs will be logic 1 and all other outputs will be 0. In the previous decoder each input 31

5 can have two values (either 0 or 1) and so there are four possible combinations of I 0 and I 1. The decoder then allows only one unique output to have value 1 for each combination of I 0 and I 1. One application of this circuit arises in addressing memory in a computer. An address code is applied to the inputs with the outputs activating separate memory registers. Thus a particular address code selects a particular memory register for access. It is also used in for example, multiple output devices like a CPU where one of several operations must be chosen or sending signals to one selected device on a line or data bus. Therefore practical decoders are generally much wider (many more outputs) than the one above. The logic circuit for the previous decoder is Wire up this circuit on the kit. Measure and record its truth table as shown below. I 0 I 1 O 3 O 2 O 1 O Write a Boolean expression for each of the outputs in terms of the inputs. 6. Memory and the clocked D flip flop In digital electronics, information is coded in logic 0 s and 1 s and each 0 or 1 is called a bit. A D flip flop is a memory circuit in which a bit can be stored. The outputs do not reflect the input conditions, unless instructed to do so. Once instructed, the outputs will remain in that state until the next instruction to change comes through. Hence, the outputs have memory. The circuit for a clocked D flip flop is The steps required to store a bit in the flip flop are as follows: 32

6 (i) The bit to be stored is applied to the D input. (ii) The CP (clock pulse) input, which is normally logic 0, is set momentarily to 1, then immediately back to logic 0. (iii) The bit applied to the input D propagates through the logic and appears at the output Q where it is stored (as long as the CP input remains 0 ). Wire the D flip flop on the kit and supply both the D and the CP inputs from switches. Perform a detailed investigation of the nature of the output Q for combinations of D and CP inputs (note that only one of the inputs should be changed at each step). Real-world uses of flip flop include the active line light on a multi-line telephone, the on indicator on a television, and caps lock and num lock indicator lights on a computer keyboard. It can also be used in digital memory devices like a CPU. Discuss the implications of the results from the D flip flop. Conclusions: Summarize your results and conclusions from this series of experiments. 33