Decoders

Decoders

• A decoder is a multiple–input, multiple–output logic circuit which converts coded inputs into coded outputs, where the input and output codes are different.

• Fig. 4.9.1 shows the general structure of the decoder circuit. As shown in Fig. 4.9.1, the encoded information is presented as n inputs producing 2ⁿ possible outputs. The 2ⁿ output values are from 0 through 2^{n – 1}.

• Usually, a decoder is provided with enable inputs to activate decoded output based on data inputs. When any one enable input is unasserted, all outputs of decoder are disabled.

1. Binary Decoder

• A decoder which has an n–bit binary input code and a one activated output out of 2ⁿ output code is called binary decoder. A binary decoder is used when it is necessary to activate exactly one of 2ⁿ outputs based on an n–bit input value.

• Fig. 4.9.2 shows 2 to 4 decoder. Here, 2 inputs are decoded into four outputs, each output representing one of the minterms of the 2 input variables. The two inverters provide the complement of the inputs, and each one of four AND gates generates one of the minterms.

Table 4.9.1 shows the truth table for a 2 to 4 decoder. As shown in the truth table, if enable input is 1 (EN = 1), one, and only one, of the outputs Y₀ to Y₃, is active for a given input. The output Y₀ is active, i.e. Y₀ =1 when inputs A = B = 0, the output Y₁ is active when inputs A = 0 and B = 1. If enable input is 0, i.e. EN = 0, then all the outputs are 0.

Example: 1

Draw the circuit for 3 to 8 decoder and explain.

Solution : Fig. 4.9.3 shows 3 to 8 line decoder. Here, 3 inputs are decoded into eight outputs, each output represent one of the minterms of the 3 input variables. The three inverters provide the complement of the inputs, and each one of the eight AND gates generates one of the minterms. Enable input is provided to activate decoded output based on data inputs A, B, and C. The table shows the truth table for 3 to 8 decoder.

2. The 74X138 3–to–8 decoder

• The 74X138 is a commercially available 3–to–8 decoder. It accepts three binary inputs (A, B, C) and when enabled, provides eight individual active low outputs (Y₀ – Y₇). The device has three enable inputs : two active low  and one active high (G₁). Fig. 4.9.4 and Table 4.9.3 show logic symbol and function table respectively.

3. The 74X139 Dual 2 to 4 Decoder

• The 74X139 consists of two independent and identical 2–to–4 decoders. The enable inputs and outputs of IC 74X139 are active low. Fig. 4.9.5 shows the logic symbol and Table 4.9.4 shows the 58A function table for IC 74X139. Table 4.9.4 shows the truth table Afor one half of a 74X139 dual 2–to–4 decoder. The truth table for other half is same as first half.

4. Expanding Cascading Decoders

• Binary decoder circuits can be connected together to form a larger decoder circuit. Fig. 4.9.6 shows the 4 × 16 decoder using two 3 × 8 decoders.

• Here, one input line (D) is used to enable/disable the decoders. When D = 0, the top decoder is enabled and the other is disabled. Thus the bottom decoder outputs are all 1s, and the top eight outputs generate minterms 0 0 0 0 to 0 1 1 1. When D =1, the enable conditions are reversed and thus bottom decoder outputs generate minterms 1000 to 1111, while the outputs of the top decoder are all 1s.

Example: 2

Design 5–to–32 decoder using one 2–to–4 and four 3–to–8 decoder ICs.

Solution :

Fig. 4.9.7 shows the construction of 5–to–32 decoder using four 74LS138s and half 74LS139. The half section of 74LS139 IC is used as a 2–to–4 decoder to decode the two higher order inputs, D and E. The four outputs of this decoder are used to enable one of the four 3 to 8 decoders. The three lower order inputs A, B and C are connected in parallel to four 3 to 8 decoders. This means that the same output pin of each of the four 3–to–8 decoders is selected but only one is enabled. The remaining enable signals of four 3–to–8 decoder ICs are connected in parallel to construct enable signals for 5–to–32 decoder.

5. Realization of Boolean Function using Decoder

• The combination of decoder and external logic gates can be used to implement single or multiple output functions. We know that decoder can have one of the two output states; either active low or active high. Let us see the significance of if these output states in the implementation of binary function.

• When decoder output is active high, it generates minterms (product terms) for input variables; i.e. it makes selected output logic 1. In such case to implement SOP function we have to take sum of selected product terms generated by decoder.

Examples for Understanding

Example: 3

Implement Boolean function F = m (1, 2, 3, 7) using 3: 8 decoder.

Solution:

Step 1: Connect function variables inputs to the decoder.

Step 2 : Logically OR the outputs correspond to present minterms to obtain the output.

Example: 4

Implement the following multiple output combinational logic using a 4 line to 16 line decoder.

Solution :

Step 1: Write the function in their minterm forms

Y₁ = Σ m (0, 3, 2, 6, 10, 11)

Y₂ = Σ m (1, 4, 5, 13)

Y₃ = Σ m (7, 14, 15)

Step 2 : Logically OR the outputs of decoder corresponding to the minterms in the functions.

Examples with Solutions

Examples: 5

Implement the following multiple output combinational logic circuit using a 4–line to 16–line decoder.

f₁ = Σ m (1, 2, 4, 7, 8, 11, 12, 13),

f₂ = Σm (2, 3, 9, 11)

f₃= Σ m (10, 12, 13, 14),

f₄ = Σ m (2, 4, 8)

Solution :

Example: 6

Design and implement a full adder circuit using a 3 : 8 decoder.

Solution :

The truth table for full adder as shown in Table 4.9.5.

Example: 7

Design an excess–3 to BCD code converter using decoder and gates.

Solution :

The truth table for excess–3 to BCD code converter is as shown in Table 4.9.6.

Realization

Examples for Practice

Example: 8

Implement the following Boolean functions using decoder and OR gates :

F₁(A,B,C,D) = Σ (2,4,7,9)

F₂(A,B,C,D) =Σ (10,13,14,15)

Example: 9

Implement the logic circuit for full subtractor using decoder.

6. Applications of Decoder

The uses of decoders are :

• Code converters

• Implementation of combinational circuits

• Address decoding

• BCD to 7–segment decoder

7. Decoder ICs

IC Number  –    Function

74138           –    3 : 8 Decoder

74139           –    Dual 2 : 4 Decoder

7442              –    BCD to decimal decoder

7447              –   BCD to 7–segment decoder

8. BCD to Decimal Decoder

• BCD decoders have four inputs and 10 outputs. The four–bit BCD input is decoded to activate one of the ten outputs. The 74XX42 is a BCD to decimal decoder. It accepts four active high BCD inputs and provides 10 independent active low outputs. Fig. 4.9.13 (a) shows pin diagram and logic symbol for IC 7442. The active low outputs of IC 7442 facilitates addressing other MSI units with active low input enables.

• The logic design of 7442 ensures that all outputs are high when binary codes greater than nine are applied to the inputs. The most significant input, A₃ produces a useful inhibit function when the 7442 is used as a 3 to 8 decoder.

• The IC 7445 is also a BCD to decimal decoder with identical pin description as that of IC 7442. However, IC 7445 provides open collector outputs.

9. BCD to Seven Segment Decoder

• In most practical applications, seven segment displays are used to give a visual indication of the output states of digital ICs such as decade counters, latches etc. These outputs are usually in four bit BCD (binary coded decimal) form, and are thus not suitable for directly driving seven segment displays. The special BCD to seven segment decoder/driver ICs are used to convert the BCD signal into a form suitable for driving these displays. In this sections, we are going to study LED and LCD decoders/drivers for seven segment displays. Let us tabulate the segments activated during each digit display.

• From Table 4.9.8 we can determine the truth table for BCD–to–7 segment decoder/driver. This truth table also depends on the construction of 7–segment display. If 7–segment display is common anode, the segment driver output must be active low to glow the segment. In case of common cathode type 7–segment display, the segment driver output must be active high to glow the segment. Table 4.9.9 and 4.9.10 show the truth tables for both BCD to 67 segment decoder/driver with common cathode display and with common anode display respectively.

• Let us design the combinational circuit for common cathode 7–segment display/driver.

K–map simplification

Logic diagram

Example: 10

Implement BCD–to–7 segment decoder for common anode using 4 : 16 decoder.

Solution :

Referring the truth table from Table 4.9.9 we can implement BCD–to–7 segment decoder for common anode as shown in Fig. 4.9.16.

Review Questions

1. Define decoder.

2. Define binary decoder.

3. Explain the working of 2: 4 binary decoder.

4. Draw a 4 × 16 decoder constructed with two 3 × 8 decoders.

5. State the procedure to implement Boolean function using decoder.

6. Mention the uses of decoders.

7. Draw the logic diagram of BCD – Decimal decoder and explain its operations.

8. Write a note on BCD to 7–segment decoder.