Visualizing Data with 7-Segment Displays

The video begins with an introduction to seven segment displays, which are used to visualize numerical data. The presenter demonstrates how to control individual segments to display decimal digits 0-9. They explain the concept of binary numbers and how to convert them to decimal using the example of the binary number 1101, which equals 13 in decimal. The video also covers the two's complement representation for negative numbers, specifically showing how the binary number 1101 becomes -3 in two's complement. The presenter then introduces a simulator with a 4-bit register capable of storing numbers from -8 to +7 and discusses the need for a 7-segment display to visualize the register's value.

The presenter dives into the process of creating a truth table for a 7-segment display to automate the lighting of correct segments for given 4-bit inputs. They list all possible 4-bit combinations and the corresponding decimal values, then determine which segments need to be lit for each value. The focus is on simplifying the logic by considering individual segments, starting with the sign segment, which correlates directly with the most significant bit. The presenter uses Boolean algebra to create expressions for each segment, demonstrating the process with examples and simplifying the expressions using Boolean rules.

The video continues with the construction of logic gates to control the seven segment display based on the simplified Boolean expressions. The presenter builds a 4-input OR gate and uses it alongside other logic gates to create the necessary logic for segment A. They test the logic in a simulation, confirming that it behaves as expected for different input values. The presenter also introduces a computer-assisted design approach, using a custom program to find a solution for the seven segment display using the least number of logic gates possible.

The presenter tests the logic design for the seven segment display using the custom solver program, which aims to minimize the number of logic gates. The program finds a solution using 19 gates, which is fewer than what the presenter could have designed manually. The video discusses the trade-offs between using fewer gates and the potential for increased delays in the circuit. The presenter tests the design in the simulator and confirms that it works correctly for displaying digits 0 through -1. They also explore using a different solver called Logic Friday and compare the results.

The video moves on to a real-world application, examining a physical chip that decodes a 4-bit input to drive a seven segment display. The presenter reviews the chip's datasheet and logic diagram, highlighting its simplicity and the independent handling of each segment. They wire up the chip and test it with different inputs to demonstrate its functionality. The presenter also discusses the process of upgrading the display for an 8-bit input and the challenges of representing the digit 9.

The presenter introduces the Double Dabble algorithm, a method for converting an 8-bit binary number into its decimal representation using Binary Coded Decimal (BCD) values. They explain the process of adding 6 to the binary number to handle the overflow at the decimal digit boundary. The video demonstrates the algorithm step by step, showing how to break down an 8-bit number into three 4-bit BCD values. The presenter then discusses implementing the Double Dabble algorithm using logic gates and the use of a solver program to assist in the design.

The video shows the process of hardwiring the Double Dabble algorithm into a custom chip. The presenter uses a visualization technique with named inputs instead of binary values to create a general solution. They detail the steps of left shifting and dabling, using multiple instances of a dabble chip to handle the algorithm's requirements. The presenter tests the chip with an 8-bit input and successfully displays the number 195 across three digit displays.

The presenter enhances the digit display by adding ripple blanking functionality to handle leading zeros and improve the visual appearance. They also address the display of negative numbers by creating a chip that negates an 8-bit number using two's complement. The video demonstrates how to integrate the negation chip and the ripple blanking into the display system, allowing for the correct representation of both positive and negative numbers. The presenter concludes by showing the complete system in action, displaying 8-bit numbers in both unsigned and two's complement formats.