1ECET 331 – Digital Integrated CircuitsChapter 6Combinational Logic FunctionsECET 331 - Digital Integrated CircuitsDecodersz Decoder• A digital circuit designed to detect the presence of particular digital state(s)• Can have one or multiple outputs• Example: A NAND gate detects the presence of ’11’ on the inputs to generate an output of 0ECET 331 - Digital Integrated CircuitsSingle Gate Decodersz Simplest form of decoderz Use single gates (AND, NAND) and inverters to detect any combination of inputsECET 331 - Digital Integrated CircuitsSingle Gate DecodersA 4-input AND detects the presence of 1111 on its inputsInputs are labeled D3, D2, D1, D0 with D3 as the MSB and D0 as the LSB ECET 331 - Digital Integrated CircuitsSingle Gate Decodersz If the inputs to a 4-input NAND are given as !D3, !D2, !D1, D0, then the NAND detects the code 0001The output is a 0 when the code 0001 is detectedz Application: this type of decoding is used for address decoding on a PC system board! = NOTThis notation is used in some HDLs and programming languagesECET 331 - Digital Integrated CircuitsExercisez Draw a single-gate decoder that detects the input state D3,D2,D1,D0 = 1100D0D1D3D2Y2ECET 331 - Digital Integrated CircuitsMultiple Output Decodersz Decoder circuits with n inputs can activate m = 2noutputs (or load circuits)z Detects multiple input combinations and generates an individual output for eachz Called an n-to-m decoder• 2-to-4 decoder• 3-to-8 decoderz Usually has an active-low enable called !GECET 331 - Digital Integrated CircuitsTruth Table for a 3-to-8 Decoder!G D2 D1 D0 !Y0 !Y1 !Y2 !Y3 !Y4 !Y5 !Y6 !Y7=================================================1 x x x 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 10 0 0 1 1 0 1 1 1 1 1 10 0 1 0 1 1 0 1 1 1 1 10 0 1 1 1 1 1 0 1 1 1 10 1 0 0 1 1 1 1 0 1 1 10 1 0 1 1 1 1 1 1 0 1 10 1 1 0 1 1 1 1 1 1 0 10 1 1 1 1 1 1 1 1 1 1 0 ECET 331 - Digital Integrated CircuitsLogic Diagram for a 3-to-8 DecoderECET 331 - Digital Integrated CircuitsSeven Segment Displaysz Seven Segment DisplayAn array of 7 independently controlled LEDs or LCD elements shaped like a figure-8 which can be used to display decimal digitsECET 331 - Digital Integrated CircuitsConventional Segment LabelingabfedcgECET 331 - Digital Integrated CircuitsHexadecimal Digit Display Convention3ECET 331 - Digital Integrated CircuitsSeven Segment Displaysz Common cathode (CC) display• A seven segment display in which the cathodes of all LEDs are grounded• Each segment is illuminated by a logic HIGH at its anode z Common anode (CA) display• A seven segment display in which the anodes of all LEDs are connected to the supply voltage• Each segment is illuminated by a logic LOW at its cathode• Most are CAECET 331 - Digital Integrated CircuitsLED Wiring ConfigurationsECET 331 - Digital Integrated CircuitsCommon Anode DisplayECET 331 - Digital Integrated CircuitsBCDz Binary Coded Decimal• A code in which each individual digit of a decimal number is represented by a 4-bit binary number• Example: 90510= 1001 0000 0101BCDECET 331 - Digital Integrated CircuitsSeven Segment Decoder / Driverz Receives a BCD input (0000 – 1001) to present a digit 0 – 9z Generates a-g outputs for each of the display LEDsECET 331 - Digital Integrated CircuitsSeven Segment Decoder DriverabfedcgInputs: D3, D2, D1, D0 = 0011 = 310Outputs: a, b, c, d, e, f, g = 1111001Common anode or cathode?4ECET 331 - Digital Integrated CircuitsSeven Segment Decoder / Driverz Decoders for a CC-SS have active high outputs (a-to-g)z Decoders for a CA-SS have active low outputs (a-to-g)z The outputs generated for input combinations 1010 to 1111 are don’t caresz The decoder can be designed with• Discrete logic• VHDL• 7447 or 7448ECET 331 - Digital Integrated CircuitsRipple Blankingz A technique used in a multi-digit numerical display that suppresses leading or trailing zeros in the display but allows internal zeros to be displayedz See textbook for more informationECET 331 - Digital Integrated CircuitsEncodersz Encoder• A digitial circuit that generates a specific code at its outputs in response to one or more active inputsz Opposite function of a decoderz Priority Encoder• An encoder that generates a specific output code according to the highest priority inputECET 331 - Digital Integrated CircuitsTruth Table for a 8-to-3 EncoderD7 D6 D5 D4 D3 D2 D1 D0 Q2 Q1 Q0===================================0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 10 0 0 0 0 1 0 0 0 1 00 0 0 0 1 0 0 0 0 1 10 0 0 1 0 0 0 0 1 0 00 0 1 0 0 0 0 0 1 0 10 1 0 0 0 0 0 0 1 1 01 0 0 0 0 0 0 0 1 1 1 ECET 331 - Digital Integrated Circuits8-to-3 Encoder Equationsz In the previous truth table, each line selected (0-7) generates its own binary code• D1 generates 001• D5 generates 101z Encoder output equations:Q2 = D4 + D5 + D6 + D7Q1 = D2 + D3 + D6 + D7Q0 = D1 + D3 + D5 + D7ECET 331 - Digital Integrated CircuitsPriority Encodersz The encoder from the previous slide would be in error if more than one input were active at the same timez Example: D3 and D5 both active• The output would be 111, not 011 or 101 as expectedz Add priority so that if D3 and D5 are active, D3 is ignored and the output code is 1015ECET 331 - Digital Integrated CircuitsPriority Encodersz Both types of designs can be implemented with:• Boolean equations • VHDL with simple concurrent logic statements (Later)z Priority encoder equations:Q2 = D7 + D6 + D5 + D4Q1 = D7 + D6 + !D5 !D4 D3 + !D5 !D4 D2Q0 = D7 + !D6 D5 + !D6 !D4 D3 + !D6!D4!D2D1ECET 331 - Digital Integrated CircuitsExerciseDetermine the correct output codes:ECET 331 - Digital Integrated CircuitsMultiplexersz A digital circuit that directs one of several digital signals to a single output depending on an input select valuez Called an N-to-1 Mux• Requires M select inputs such that 2M= N• Example: 4-to-1 mux requires 2 select inputs (S1, S0)ECET 331 - Digital Integrated Circuits4-to-1 Mux SymbolECET 331 - Digital Integrated CircuitsMultiplexer Logic (1)z 4-to-1 mux logic equation:Y = D0(!S1!S0) + D1(!S1S0) + D2(S1!S0) + D3(S1S0)z This format can be expanded to any size muxz (Later)