L2.2 Lecture 3

L2.3: Designing standard logic circuits. VHDL: Decoders and encoders [P2] Flat (single VHDL file) plans: structural plan A / behavioural plan B

L2.4 [24/9]

1.7.4. Binary decoder

1.7.4.1. Dec_3_8, Dec_4_16

Discussing binary decoder basics and specifications rec.. From our concept map: 1) Symbol, (2) truth table or equations, (3) timing diagram, (4) commercial chip, (5) internal design (Plan A, B, C1 or C2), (6) how to expand them (Plan C2 in P3)?

Fig. 1. Generic binary decoder symbol.

Fig. 2 shown the symbol and truth table when n = 3, it is a Dec_3_8 device.

Fig. 2. Dec_3_8 truth table.

1.7.4.2. Design examples

- Plan A. This tutorial is the complete design using VHDL tools of the decoder Dec_3_8 using equations.

Fig. 3. Structural equations inferred inspecting the truth table.

Finally, we can draw this eight equations based on canonical minterms as represented in Fig. 4.

Fig. 4. Circuit based on minterms.

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- Plan B. This tutorial is the complete design using VHDL tools of the decoder Dec_3_8 using the truth table, algorithm flowchart or any other high-level interpretation.

Fig. 5. Circuit algorithm.

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1.7.4.3. Decoder expansion circuits (plan C2)

1.7.4.4. Commercial chips

74HCT138, etc.

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1.7.5. Binary encoders (priority high)

1.7.5.1. Enc_8_3, Enc_10_4

The symbol for an Enc_8_3 is represented in Fig. 6 and its truth table in Fig. 7.

Fig. 6. Circuit Enc_8_3.

This truth table is 512 rows long. It can be written in a compact form using don't care terms as shownin Fig. 7.

Fig. 7. Enc_8_3 truth table.

And an example of timing diagram is represented in Fig. 8.

Fig. 8. Enc_8_3 timing diagram example.

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We can start thinking now on design plans, for instance Plan A trying to deduce some equations.

Fig. 9. Some equations after exploring the truth table. Using Minilog will generate the complete list of output functions in SoP or PoS form, ready for VHDL translation as Enc_8_3.vhd source file.

1.7.5.2. Design examples

- Plan A. Discussion of the binary encoder Enc_10_4 using equations.

- Plan B. Discussion of the binary encoder Enc_10_4 using the truth table, algorithm or any other high-level interpretation.

1.7.5.3. Encoder expansion circuits (plan C2)

1.7.5.4. Commercial chips

74HCT148, 74LS147, CMOS 4532B, etc.

 

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Exercise: Adapt, using logic gates if necessary, the 74HCT138 commercial chip to the symbol in picture Fig. 2.

 

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