This document discusses decoders and provides details about binary coded decimal (BCD) to decimal decoders. It explains that decoders recognize various input combinations and provide corresponding outputs. A BCD to decimal decoder specifically provides decimal outputs from a binary coded input. The document then presents the circuit design and operation of a BCD to decimal decoder using AND gates. It analyzes how the circuit decodes input codes to activate the proper decimal output and discusses how faults could be identified by analyzing input-output relationships.

1. THE DECODER
PREPARED BY: JOHN LEXTER L. EMBERADOR
BSIE-201 ELECTRONICS
SUBMITTED TO: MS. JANICE G. DULCE
DATE SUBMITTED: AUGUST 13,2012

2. BASIC CONCEPT
1. 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. 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. • 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.

6. • 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.

8. • 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.

10. • 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.

11. IDENTIFYING BCD TO
DECIMAL DECODER
• A BCD to Decimal Decoder circuit
is shown in Figure 6-2.

13. • 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).

14. • 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).

15. • 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.

16. 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.

18. • 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.

20. POST-TEST
I.IDENTIFICATION
1.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.

21. 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.
1.0100
2.1001
3.0011
4.1100
5.1010

22. III. Give the Output Decimal Number of the
following Digital Logic State.
1.DC̅BA
2.D̅CBA̅
3.D̅C̅B̅A
4.DC̅BA̅
5.DCB̅A
IV. Give the Output Decoder of the following
Inputs in the general rule 2N.
1.N=3
2.N=5
3.N=8
4.N=10
5.N=12

23. KEY ANSWERS
I.
1.ENCODER
2.2N
3.BCD TO DECIMAL DECODER
4.AND OPERATION
5.INCORRECT FOR SEVERAL INPUTS
II.
1.D̅CB̅A̅
2.DC̅B̅A
3.D̅C̅BA
4.DCB̅A̅
5.DC̅BA̅

24. KEY ANSWERS
III.
1.11
2.6
3.1
4.10
5.13
IV.
1.23 = 8
2.25 =32
3.28 =256
4.210 =1024
5.212 =4096