Digital Electronics - 08 Combinational Circuits, MSI and PLD.pdf

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11/6/2020 FERNANDO VICTOR V. DE VERA, ECE, M.Tech 1 Logic Circuits COMBINATIONAL LOGIC Output is dependent on present input only. Has logic gates only. EQUENTIAL LOGIC Output is dependent on present input and past outputs. Has logic gates and memory elements. Combinational Logic Circuit The output states is dependent only on present input states. The output changes at any time the input changes state. No memory elements is required. Combinational Circuit n inputs m outputs 33 34
11/6/2020 FERNANDO VICTOR V. DE VERA, ECE, M.Tech 2 equential Logic Circuit Output is dependent on present input and past outputs. Needs memory elements. May contain timing devices (clock pulses). Combinational Circuit n inputs m outputs Memory Elements ANALY I of a Combinational Circuit The functions of all output with respect to the input variables is derived. A truth table is derived to determine the output behavior of the circuit. 35 36
11/6/2020 FERNANDO VICTOR V. DE VERA, ECE, M.Tech 3 Example No. Analyze the given combinational circuit. Write the simplified functions of F1 and F2 and create the truth table. Practice Exercise No. Write the standard and canonical forms of the outputs F1 and F2: 37 38
11/6/2020 FERNANDO VICTOR V. DE VERA, ECE, M.Tech 4 Practice Exercise No. Write the standard and canonical forms of the outputs F and G: DE IGN of a Combinational Circuit tate (Understand) the problem. Determine the needed INPUT and OUTPUT variables, and assign literals to them. Derive the truth table for every output. implify the Boolean functions of each output Using Kmap, Boolean algebra, etc Implement using OP, PO , universal gates, etc Draw the Logic diagram. 39 40
11/6/2020 FERNANDO VICTOR V. DE VERA, ECE, M.Tech 5 Example No. Design a combinational circuit with 4 inputs and a single output. The output is 1 if there are equal or greater 0’s compared with 1’s at the input. INPUT VARIABLES OUTPUT(S) ABCD Y 0000 1 0001 1 0010 1 0011 1 0100 1 0101 1 0110 1 0111 0 1000 1 1001 1 1010 1 1011 0 1100 1 1101 0 1110 0 1111 0 OLUTION to Example: OUTPUT FUNCTION simplification: Note: Different implementation yields different gate counts. AB\CD 00 01 11 10 00 1 1 1 1 01 1 1 1 11 1 10 1 1 1 AB\CD 00 01 11 10 00 01 0 11 0 0 0 10 0 41 42
11/6/2020 FERNANDO VICTOR V. DE VERA, ECE, M.Tech 6 OLUTION to Example: (cont.) AB\CD 00 01 11 10 00 01 0 11 0 0 0 10 0 Y = (A’+B’+C’) (A’+B’+D’) (A’+C’+D’) (B’+C’+D’) 43 44
11/6/2020 FERNANDO VICTOR V. DE VERA, ECE, M.Tech 7 Example No. Code Converter Design a combinational logic circuit that converts 84-2-1 to a Gray Code of equal bit length. INPUT: 84-2-1 OUTPUT: Gray ABCD Y 3 Y 2 Y 1 Y 0 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 DECIMAL CODES BCD 2421 XS3 84-2-1 Biquinary 8421 2421 (+3) 84-2-1 5043210 0 0000 0000 0011 0000 0100001 1 0001 0001 0100 0111 0100010 2 0010 0010 0101 0110 0100100 3 0011 0011 0110 0101 0101000 4 0100 0100 0111 0100 0110000 5 0101 1011 1000 1011 1000001 6 0110 1100 1001 1010 1000010 7 0111 1101 1010 1001 1000100 8 1000 1110 1011 1000 1001000 9 1001 1111 1100 1111 1010000 Unused 1010 0101 0000 0001 1011 0110 0001 0010 1100 0111 0010 0011 1101 1000 1101 1100 1110 1001 1110 1101 1111 1010 1111 1110 45 46
11/6/2020 FERNANDO VICTOR V. DE VERA, ECE, M.Tech 8 Gray Code A unique coding where the transition from one number to another causes only one bit to change.

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