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Problem 2: Seven-segment displays are very common output display devices that are used in many common application like clocks, radios, calculators, odometers, etc. It is one of the easiest way to implement a numeric output for a digital circuit for a hexadecimal base. It takes a four-bit binary numeric input, and uses a display made of seven long, thin LEDS arranged in a parttern of an eight to create to signals necessary to drive the display. If we label the seven LEDS as (a, b, c, d, e, f, g), these seven outputs of the decoder select the corresponding segments in the display, as it shown below:

Problem 2: Seven-segment displays are very common output display devices that are used in many common application like clocks, radios, calculators, odometers, etc. It is one of the easiest way to implement a numeric output for a digital circuit for a hexadecimal base. It takes a four-bit binary numeric input, and uses a display made of seven long, thin LEDS arranged in a parttern of an eight to create to signals necessary to drive the display. If we label the seven LEDS as (a, b, c, d, e, f, g), these seven outputs of the decoder select the corresponding segments in the display, as it shown below:

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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**Problem 2: Seven-Segment Display** Seven-segment displays are common output devices used in applications like clocks, radios, calculators, and odometers. They provide an easy method to produce numeric output for digital circuits, especially for hexadecimal bases. The display involves a four-bit binary input and utilizes seven thin LEDs arranged in a pattern to produce the necessary signals for displaying numbers. In the depiction of segments as labeled \( a, b, c, d, e, f, g \), these outputs from the decoder select the necessary segments to display the corresponding number, as illustrated: **Diagram Description:** The diagram shows numbers 0 to F, each represented using a seven-segment layout. Each digit highlights different segments: - For instance, the number "0" typically lights up segments \( a, b, c, d, e, \) and \( f \). - The number "1" lights up segments \( b \) and \( c \), and so on. The diagram visualizes the hexadecimal representation from 0 to F, with each value depicted by lighting up the relevant segments. **Tasks:** 1. **Truth Table:** - Create a truth table for a circuit managing segment "c" of the seven-segment display. - Highlight which numbers activate the "c" segment (e.g., "0", "1", "3"). 2. **Karnaugh Map Reduction:** - Utilize Karnaugh maps to attain a simplified Boolean function for the seven-segment decoder, minimizing gate usage in a sum-of-products form. 3. **Circuit Implementation:** - Build the circuit using a simulator, employing only NAND and NOT gates. 4. **Verification:** - Confirm the circuit's accuracy with the truth table. - Connect directly to inputs and compare LED results with values shown on the display. - Ensure the ground input of the seven-segment display is connected. Submit the truth table and Karnaugh map from tasks (a) and (b), alongside screenshots of your simulation proving segment "c" activation for at least two different input sets.
Transcribed Image Text:**Problem 2: Seven-Segment Display** Seven-segment displays are common output devices used in applications like clocks, radios, calculators, and odometers. They provide an easy method to produce numeric output for digital circuits, especially for hexadecimal bases. The display involves a four-bit binary input and utilizes seven thin LEDs arranged in a pattern to produce the necessary signals for displaying numbers. In the depiction of segments as labeled \( a, b, c, d, e, f, g \), these outputs from the decoder select the necessary segments to display the corresponding number, as illustrated: **Diagram Description:** The diagram shows numbers 0 to F, each represented using a seven-segment layout. Each digit highlights different segments: - For instance, the number "0" typically lights up segments \( a, b, c, d, e, \) and \( f \). - The number "1" lights up segments \( b \) and \( c \), and so on. The diagram visualizes the hexadecimal representation from 0 to F, with each value depicted by lighting up the relevant segments. **Tasks:** 1. **Truth Table:** - Create a truth table for a circuit managing segment "c" of the seven-segment display. - Highlight which numbers activate the "c" segment (e.g., "0", "1", "3"). 2. **Karnaugh Map Reduction:** - Utilize Karnaugh maps to attain a simplified Boolean function for the seven-segment decoder, minimizing gate usage in a sum-of-products form. 3. **Circuit Implementation:** - Build the circuit using a simulator, employing only NAND and NOT gates. 4. **Verification:** - Confirm the circuit's accuracy with the truth table. - Connect directly to inputs and compare LED results with values shown on the display. - Ensure the ground input of the seven-segment display is connected. Submit the truth table and Karnaugh map from tasks (a) and (b), alongside screenshots of your simulation proving segment "c" activation for at least two different input sets.
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