chap4(4_in_1)

chap4(4_in_1) - ELEC151 Digital Circuits and Systems...

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ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 4-1 Lecture Note #4 Combinational Logic • Combinational circuits – Design procedure and analysis skill 4-1, 4-2, 4-3 • Circuit examples – Binary adder and subtractor 4-4 – Binary multiplier 4-6 – magnitude comparator 4-7 – Decoder and encoder 4-8, 4-9 – Multiplexer and demultiplexer 4-10 • Circuit technologies – TTL AND-OR-Inverter (AOI) 10-5 – CMOS transmission gates 10-9 • Reading Assignments: – Chapter 4 – Section 10-5, 10-9 ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 4-2 Combinational Circuit Outputs Inputs Next-state Combinational Circuit Output Combinational Circuit Finite States Inputs Outputs Feedbacks Clocks Combinational vs Sequential Logic • Combinational Logic – Outputs are solely determined by the inputs – Represented by a truth table • Sequential Logic – There are feedbacks and clocks – Outputs are determined by the inputs and feedbacks at clocks – Represented by a state-transition diagram or flow chart ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 4-3 Design Procedures: • Understand the project specifications • Express the input and output relations in truth table In general (or multi-level logic), Derive the Boolean Expressions from the truth table Use Laws of Boolean Algebra for logic simplification In two-level logic, Re-express the truth table in the K-Map Read out the simplified Boolean expressions from the K-map • Map the simplified Boolean expressions to digital circuits – CAD tool simulation • Implement the design by components – Selections of components • Digital design is more of an art than a science – The creative spirit is critical in combining primitive elements in new ways to achieve a desired function. ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 4-4 Code Conversion Example • Understand the specifications: BCD to Excess-3 – Binary Coded Decimal (BCD) has 4 bits and 10 numbers – Excess-3 code has a value that excesses 3 of BCD • Express in a truth table –(ABCD ) 2 for the inputs and (WXYZ) 2 for the outputs BCD code Excess-3 code A B C D W X Y Z 0 0 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 0
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ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 4-5 Code Conversion Example, K-map • Re-express in the K-map – Note the ABCD placement – Incompletely specified functions • Read out the most simplified Boolean expressions – How many literals? » 1+4+7+5=17 – How many TTL gates? – How many equivalent gates? ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 4-6 Code Conversion Example, Circuits • Map the Boolean expressions to digital circuit – in AND-OR (two-level), or some other forms (multi-level) – The algebraical manipulation is possible, but not recommended ELEC151 Digital Circuits and Systems Ho-Chi Huang, Lecture Notes, No. 4-7
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This note was uploaded on 09/16/2010 for the course ELEC 151 taught by Professor Cy during the Spring '10 term at HKUST.

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chap4(4_in_1) - ELEC151 Digital Circuits and Systems...

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