Seven-Segment Decoders Lesson 10 PDF

Analog representation for binary coded decimal Seven-Segment Decoders and Seven-segment display Seven-segment display: An array of seven independently controlled light-emitting diode (LED) or liquid crystal display (LCD) elements, shaped like a figure-8, which can be used to display decimal...

Analog representation for binary coded decimal Seven-Segment Decoders and Seven-segment display Seven-segment display: An array of seven independently controlled light-emitting diode (LED) or liquid crystal display (LCD) elements, shaped like a figure-8, which can be used to display decimal digits and other characters by turning on the appropriate elements. Arrangement of segments for “Seven-segment display”: The electrical requirements for an LED circuit are simple. Since an LED is a diode, it conducts when its anode is positive with respect to its cathode, as shown in Figure a. Seven-segment displays are configured as common anode (active-LOW inputs) or common cathode (active-HIGH segments). Common cathode display A seven-segment display in which the cathodes of all LEDs are connected together and grounded. A logic HIGH illuminates a segment when applied to its anode, as shown in Figure b. Common anode display A seven-segment LED display where the anodes of all the LEDs are connected to the circuit supply voltage. Each segment is illuminated by a logic LOW at its cathode, as shown in Figure c. 1 Dr. Attia The diodes could be physically laid out in a common anode display: 2 Dr. Attia  The two types of displays allow the use of either active HIGH or active LOW circuits to drive the LEDs, thus giving the designer some flexibility. However, it should be noted that the majority of seven-segment decoders are for common-anode displays. Block diagram of 7-segment decoding logic and display: Decoder: A digital circuit designed to detect the presence of a particular digital state. The general function of a decoder is to activate one or more circuit outputs upon detection of a particular digital state. The simplest decoder is a single logic gate, such as a NAND or AND, whose output activates when all its inputs are HIGH. The two such decoders: Both of which detect an input 𝐷3 𝐷2 𝐷1 𝐷0 = 1111. The decoder in Figure a generates a logic HIGH when its input is 1111. The decoder in Figure b responds to the same input, but makes the output LOW instead. 3 Dr. Attia  When combined with one or more inverters, a NAND or AND can detect any unique combination of binary input values. Example: Below figure shows three single-gate decoders. For each one, state the output active level and the input code that activates the decoder. Also write the Boolean expression of each output. Solution Each decoder is a NAND or AND gate. For each of these gates, the output is active when all inputs are HIGH. Because of the inverters, each circuit has a different code that fulfils this requirement. Figure a: Output: Active LOW Input code:𝐷3 𝐷2 𝐷1 𝐷0 = 1001. 𝑌̅ = 𝐷3 𝐷 ̅2 𝐷 ̅1 𝐷0. Figure b: Output: Active LOW Input code:𝐷2 𝐷1 𝐷0 = 001. 𝑌̅ = 𝐷 ̅2 𝐷 ̅1 𝐷0. Figure c: Output: Active HIGH Input code: 𝐷3 𝐷2 𝐷1 𝐷0 = 1010. 𝑌 = 𝐷3 𝐷̅2 𝐷1 𝐷 ̅0 BCD (Binary coded decimal): A code in which each individual digit of a decimal number is represented by a 4-bit binary number (e.g., 905 (decimal) = 1001 0000 0101 (BCD)). A BCD-to-seven-segment decoder is a circuit with a 4-bit input for a BCD digit and seven outputs for segment selection. To display a number, the decoder must translate the input bits to a combination of active outputs. For example, the input digit 𝐷3 𝐷2 𝐷1 𝐷0 = 0000 must illuminate segments a, b, c, d, e, and 4 Dr. Attia  f to display the digit 0. We can make a truth table for each of the outputs, showing which must be active for every digit we wish to display. The truth table for a common-anode decoder (active LOW outputs) is given as: Truth Table for Common Anode BCD-to-seven-segment Decoder The illumination of each segment is determined by a Boolean function of the input variables, DCBA. From the truth table: ̅ 𝐶̅ 𝐵̅ 𝐴 + 𝑎=𝐷 ̅ 𝐶𝐵̅𝐴̅ 𝐷 ̅ 𝐶𝐵̅ 𝐴 + 𝑏=𝐷 ̅ 𝐶𝐵𝐴̅ 𝐷 ̅ 𝐶̅ 𝐵 𝐴̅ 𝑐=𝐷 ̅ 𝐶̅ 𝐵̅ 𝐴 + 𝑑=𝐷 ̅ 𝐶𝐵̅𝐴̅ + 𝐷 ̅ 𝐶𝐵𝐴 𝐷 ̅ 𝐶̅ 𝐵̅ 𝐴 + 𝑒=𝐷 ̅ 𝐶̅ 𝐵𝐴 + 𝐷 ̅ 𝐶𝐵̅𝐴̅ + 𝐷 𝐷 ̅ 𝐶𝐵𝐴 + 𝐷𝐶̅ 𝐵̅𝐴 ̅ 𝐶𝐵̅𝐴 + 𝐷 ̅ 𝐶̅ 𝐵̅ 𝐴 + 𝑓=𝐷 ̅ 𝐶̅ 𝐵𝐴̅ + 𝐷 𝐷̅ 𝐶̅ 𝐵𝐴 + 𝐷 ̅ 𝐶𝐵𝐴 ̅ 𝐶̅ 𝐵̅ 𝐴̅ + 𝑔=𝐷 ̅ 𝐶̅ 𝐵̅𝐴 + 𝐷 ̅ 𝐶𝐵𝐴 𝐷 5 Dr. Attia The corresponding partial decoder for segment e is shown in Figure: The resultant function is: ̅ 𝐶̅ 𝐵̅ 𝐴 + 𝐷 𝑒=𝐷 ̅ 𝐶̅ 𝐵𝐴 + 𝐷 ̅ 𝐶𝐵̅𝐴̅ + 𝐷 ̅ 𝐶𝐵𝐴 + 𝐷𝐶̅ 𝐵̅𝐴 ̅ 𝐶𝐵̅𝐴 + 𝐷 (Since the display is active-LOW, this means segment e is OFF for digits 1, 3, 4, 5, 7 and 9.) We could do a similar analysis for each of the other segments. 6 Dr. Attia  Example for the decimal digit 5: 7 Dr. Attia  The truth table for a common-cathode decoder (active HIGH outputs) is given as: Truth Table for Common Cathode BCD-to-seven-segment Decoder The illumination of each segment is determined by a Boolean function of the input variables, DCBA. From the truth table: 𝑎=𝐷̅ 𝐶̅ 𝐵̅𝐴̅ + 𝐷̅ 𝐶̅ 𝐵𝐴̅ + 𝐷 ̅ 𝐶̅ 𝐵𝐴 + 𝐷 ̅ 𝐶𝐵̅𝐴 + 𝐷̅ 𝐶𝐵𝐴̅ + 𝐷̅ 𝐶𝐵𝐴 + 𝐷𝐶̅ 𝐵̅𝐴̅ + 𝐷𝐶̅ 𝐵̅𝐴 𝑏=𝐷̅ 𝐶̅ 𝐵̅𝐴̅ + 𝐷̅ 𝐶̅ 𝐵̅𝐴 + 𝐷 ̅ 𝐶̅ 𝐵 𝐴̅ + 𝐷 ̅ 𝐶̅ 𝐵𝐴 + 𝐷 ̅ 𝐶𝐵̅𝐴̅ + 𝐷 ̅ 𝐶𝐵𝐴 + 𝐷𝐶̅ 𝐵̅𝐴̅ + 𝐷𝐶̅ 𝐵̅𝐴 𝑐=𝐷̅ 𝐶̅ 𝐵̅ 𝐴̅ + 𝐷 ̅ 𝐶̅ 𝐵̅𝐴 + 𝐷 ̅ 𝐶̅ 𝐵𝐴 + 𝐷 ̅ 𝐶𝐵̅𝐴̅ + 𝐷 ̅ 𝐶𝐵̅𝐴 + 𝐷̅ 𝐶𝐵𝐴̅ + ̅ 𝐶𝐵𝐴 + 𝐷𝐶̅ 𝐵̅𝐴̅ + 𝐷𝐶̅ 𝐵̅𝐴 𝐷 𝑑=𝐷̅ 𝐶̅ 𝐵̅ 𝐴̅ + 𝐷 ̅ 𝐶̅ 𝐵𝐴̅ + 𝐷 ̅ 𝐶̅ 𝐵𝐴 + 𝐷 ̅ 𝐶𝐵̅𝐴 + 𝐷̅ 𝐶𝐵𝐴̅ + 𝐷𝐶̅ 𝐵̅𝐴̅ + 𝐷𝐶̅ 𝐵̅𝐴 𝑒=𝐷̅ 𝐶̅ 𝐵̅ 𝐴̅ + 𝐷 ̅ 𝐶̅ 𝐵𝐴̅ + 𝐷 ̅ 𝐶𝐵𝐴̅ + 𝐷𝐶̅ 𝐵̅𝐴̅ ̅ 𝐶̅ 𝐵̅𝐴̅ + 𝐷 𝑓= 𝐷 ̅ 𝐶𝐵̅𝐴̅ + 𝐷̅ 𝐶𝐵̅𝐴 + 𝐷 ̅ 𝐶𝐵𝐴̅ + 𝐷𝐶̅ 𝐵̅𝐴̅ + 𝐷𝐶̅ 𝐵̅𝐴 𝑔=𝐷̅ 𝐶̅ 𝐵 𝐴̅ + 𝐷̅ 𝐶̅ 𝐵𝐴 + 𝐷̅ 𝐶𝐵̅𝐴̅ + 𝐷 ̅ 𝐶𝐵̅𝐴 + 𝐷̅ 𝐶𝐵𝐴̅ + 𝐷𝐶̅ 𝐵̅𝐴̅ + 𝐷𝐶̅ 𝐵̅ 𝐴 8 Dr. Attia Logic diagram for Common Cathode BCD-to-7-segment decoder: Contact points shown on the above diagram for each of the outputs indicate which must be active for every digit we wish to display. Exercise: Draw a logic circuit of a partial decoder for segment e of Common-Cathode LED display and write its Boolean function. Compare with that circuit above for Common-Anode LED display. Exercise: Draw a Logic diagram for Common-Anode BCD-to-7- segment decoder and determine on the diagram for each of the outputs which must be active for every digit we wish to display corresponding to the truth table. 9 Dr. Attia Application Learning to count in binary will help you to basically understand how digital circuits can be used to count events. This can be anything from counting items on an assembly line to counting operations in a computer. Let's take a simple example of counting tennis balls going into a box from a conveyor belt. Assume that nine balls are to go into each box. The counter in the following Figure counts the pulses from a sensor that detects the passing of a ball and produces a sequence of logic levels (digital waveforms) on each of its four parallel outputs. Each set of logic levels represents a 4-bit binary number (HIGH = 1 and LOW= 0), as indicated. As the decoder receives these waveforms, it decodes each set of four bits and converts it to the corresponding decimal number in the 7-segment display. When the counter gets to the binary state of 1001, it has counted nine tennis balls, the display shows decimal 9, and a new box is moved under the conveyor. Then the counter goes back to its zero stat (0000), and the process starts over. (The number 9 was used only in the interest of single- digit simplicity). Illustration of a simple binary counting application. 10 Dr. Attia