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Decoders and Multiplexers Prof. Sin-Min Lee Department of Computer Science San Jose State University

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Decoders A combinational circuit that converts binary info from n inputs into a max. of 2 n unique objects. N - to - m decoders: given n inputs, it outputs m <= 2 n minterms. Note the ``3'' with a slash, which signifies a three bit input. This notation represents three (1-bit) wires. A decoder with n input bits, produces 2^n output bits.

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Combinational circuit implementation using Decoders We can use decoders to express Boolean functions. Any Boolean function can be expressed as a sum of products(minterms). So, we can use decoders to produce the minterms and OR gates to produce their logical sum.

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Design a digital circuit which compares the magnitude of two 2-bit numbers and. It has one output f 1 such that f 1 =1 if and only if X > Y. Step 1: Derive the truth table that describes the relation between f 1 and the inputs x 1, x 2, y 1, and y 2, where x 1 and y 1 each denotes the most significant bit of X and Y respectively. Comparator

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Example: expressing full adder with decoder We have 3 inputs. So, we use the 3-to-8 decoder to generate the minterms. Then we OR 1, 2, 4, 7 and 3,5,6,7 according to the Boolean equations: –S(X,Y,Z) = Sm(1,2,4,7) –C(X,Y,Z) = Sm(3,5,6,7)

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Step 2: Now use the 4-variable K-map to derive the minimal sum of product (SOP) expression for f 1.

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Implementation using MUXs: Now we implement the output f 1 using an 8x1MUX. Selection inputs to the MUX are x 2 y 1 y 2 (that is, if x 2 y 1 y 2 =001, input I 1 of the MUX is selected). The implementation table is tabulated as

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Implementation using decoders: Now we implement the output f 1 using an decoder and 3-input OR gates.

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Decoders A B C O7 O6 O5 O4 O3 O2 O1 O0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 A B C O0 O1 O2 O3 O4 O5 O6 O7 Inputs Outputs

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Multiplexers 2**n data inputs, n control input, one data output Data inputs selected by control are gated are gated to output Each AND gate gets 3 control and one data input, selects input based on control OR gate adds all selected inputs

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Majority Function using a Multiplxer Each input wired to 1 or 0 If 0 in table ground Else connect to Vcc. Check if it works!

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Other Users of Multiplexers Parallel to Serial Conversion Put 8 bit data in input lines Step through 000 to 111 in control lines to select inputs serially Used in serializing device inputs such as key board inputs over telephone lines Inverse operation: Demultiplexing routes single serial input into multiple outputs depending on value of control lines

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Decoders Selects one of 2**n inputs Each AND gate implements one Boolean expression ABC etc.

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Comparators 4 address words, A, B compared. Output (A =B) Users XOR gates: 1 iff both inputs are same

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Programmable Logic Arrays (PLA) Used to form Sums of products Select inputs by burning out fuses Example has 12 inputs, 6 outputs, PWR and GND

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PGA Computing Majority function Can burn appropriate fuses to fabricate Majority function from a PGA. Choose –3 inputs, 4 AND gates and 1 OR gate –Burn appropriate fuses Which one is best for Majority: –SSI with 4 gates –1 MSI multiplexer –PLA: more efficient

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