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# The decoder

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### The decoder

1. 1. THE DECODERPREPARED BY: JOHN LEXTER L. EMBERADOR BSIE-201 ELECTRONICS SUBMITTED TO: MS. JANICE G. DULCE DATE SUBMITTED: AUGUST 13,2012
2. 2. BASIC CONCEPT1. A DECODER circuit is used to recognize the various combinations of an input word and provide an output for each combination.2.If an input word contains N “bits” then the decoder can have 2N outputs.3.A combination of gates can be used to construct a decoder circuit.4.A BCD to Decimal Decoder is used to provide decimal information from a binary coded input.
3. 3. INTRODUCTORY INFORMATION● A decoder can be thought of in the opposite sense as an encoder. In encoder, the decimal number was coded so that digital operation could be performed using binary numbers. The binary information which was processed in a coded form by digital circuits can be recognized or decoded by a decoder circuit.
4. 4. • The resulting outputs will represent the original input code. A typical example of this is a BCD to Decimal Decoder.• Table 6-1 shows the decimal equivalents of a four “bit” binary word. In addition it shows the states of the four inputs ABCD to a decider required to represent decimal numbers 0 through 9.
5. 5. • Notice that the table shows a four bit binary word can produce up to 16 distinct outputs. A general rule for decoders is that when the number of inputs is equal to a number N, the decoder will produce 2N outputs.• For table 6-1, N equals 4 and there will be 24 or 16 outputs. However, we need only to produce one digit of a decimal number or the decimal symbols 0 through 9.• Figure 6-1 shows a typical application for a BCD to Decimal decoder.
6. 6. • The functions shown will provide a two digit numeric readout using Nixie ® tubes as display devices.• The requirement is to provide a signal to energize the proper number, 0 through 9 of the Nixie Tube, when a certain number of input pulses are counted in Binary Coded Decimal form.
7. 7. • That is, a four bit BCD word exist as inputs to the decoder and outputs 0 through 9 are required for Nixie tube drivers. The circuitry for a second digit is shown in block form, is identical to the first digit and accepts a pulse following each 0 through 9 sequence of the first digit.• Simultaneously, a reset pulse within the counter will initiate the BCD code 0000 and the numeric 0 output. The system shown represents a two digit counter that will count up to 99 and then reset to 0.
8. 8. IDENTIFYING BCD TO DECIMAL DECODER• A BCD to Decimal Decoder circuit is shown in Figure 6-2.
9. 9. • As we can see from the figure 6-1 and table 6-1, the decoding process essentially requires the logic AND operation. The table and figure show the BCD inputs required to produce the decimal outputs 0 through 9.• Recalling that all HI logic states are required to produce HI outputs, notice that the circuit shows inverters to provide HI inputs at the AND gates when BCD inputs A,B,C and D are L0 (A̅,B̅,C̅ and D̅).
10. 10. • Also notice that all lines of the circuit are identified showing the input state and code place value for each input bit. For example, if the BCD code for the number 6 were to be decoded the input from table 6-1 would be 0110 or D̅CBA̅. In figure 6-2 a L0 at the input to INVERTERS (D) and (A)(circles) will produce a HI at these outputs (no circles). The remaining 2 input bits required to produce a HI output from AND gate (6), namely C and B are HI and will activate the gate without inversion. Looking at the input lines to gate (6) will verify that a HI will exist on all inputs for the code 0110 or D̅CBA̅ with place values (8̅421̅).
11. 11. • All remaining gates of figure 6- 2 can be analyzed in the same manner. A HI at the outputs would provide the signal required to activate a numeric readout.
12. 12. ANALYZING TROUBLE SYMPTOMS OF DECODER CIRCUIT AND ITS SIGNAL• Decoder circuit operation can be checked by noting the inputs and outputs. An analysis of the inputs and outputs usually indicates location of the circuit fault. Then, logic probe circuit tracing can be employed to isolate the exact location of the fault.• For example, in the BCD decoder circuit of figure 6-3, a defective gate will affect only one decimal output, the gate might be open or shorted, in which case the output would remain permanently L0 or HI.
13. 13. • On the other hand, if one of the INVERTERS were defective, the decimal outputs would be incorrect for several inputs. If the C̅ inverter were in a permanently HI state, for example, then as the BCD inputs proceeded through a count from 000 to 111, we would get the outputs shown in table 6-3.
14. 14. POST-TESTI.IDENTIFICATION1.A DECODER can be thought of in the opposite sense as an __________.2.What is the general rule for decoder, if the number of the inputs is equal to a number N, the decoder will produce _________ outputs.3.__________ is used to provide decimal information from a binary coded input.
15. 15. 4.In the figure 6-1 and table 6-1, the decoding process essentially requires what kind of logic operation?5.If one of the INVERTERS were defective, what would happened to the decimal output of a decoder circuit?II. Rewrite the following Input Binary Code into Digital Logic State.1.01002.10013.00114.11005.1010
16. 16. III. Give the Output Decimal Number of the following Digital Logic State.1.DC̅BA2.D̅CBA̅3.D̅C̅B̅A4.DC̅BA̅5.DCB̅AIV. Give the Output Decoder of the following Inputs in the general rule 2N.1.N=32.N=53.N=84.N=105.N=12
17. 17. KEY ANSWERSI.1.ENCODER2.2N3.BCD TO DECIMAL DECODER4.AND OPERATION5.INCORRECT FOR SEVERAL INPUTSII.1.D̅CB̅A̅2.DC̅B̅A3.D̅C̅BA4.DCB̅A̅5.DC̅BA̅
18. 18. KEY ANSWERSIII.1.112.63.14.105.13IV.1.23 = 82.25 =323.28 =2564.210 =10245.212 =4096