Seven-Segment Display A seven-segment display (SSD) is an electronic device used for displaying numerical values. The device typically consists of seven segments arranged in a figure 8. Any digit, as well as some alphabet letters, can be displayed when the correct segments are activated. An example of an SSD as well as possible outputs can be seen in Figure 3. 889 Figure 3 - Seven-Segment Display with Numeric Outputs Workstation Details PC Desktop / Laptop with LabVIEW FPGA 2013 Lab Procedure Task www Using the truth table created in the Pre-Lab Preparation, design minimal logic circuits in LabVIEW FPGA for each segment output of the SSD using the Karnaugh mapping technique discussed in the Background and Theory section. Requirements • Implement the design as a subVI. Create a top-level VI design that uses an instance of the SSD subVI. Use slide switches as inputs and tie outputs to the appropriate I/O port pins connected to the seven-segment display module. (Refer to the SSD reference manual). • Create a test plan to verify the design. Debug when necessary. Demonstrate to lab instructor. Tips • • Keep the schematic design neat and easy to understand (i.e. clean wiring, text labels, etc) in order to make debugging simpler. Use toggle switches as inputs and tie the outputs to the appropriate I/O pins connected to the seven-segment display module. (Refer to the SSD reference manual). • Create a test plan to verify the design. Debug when necessary. • Square LEDs can be resized to appear as a seven segment display 8 Weight 4 Weight 2 Weight 1 Weight J A F B G D Lab 2 - Karnaugh Maps Due Date: Sunday of Week 5 by 11:55 PM In this lab experiment, the student will design a minimized, seven-segment display decoder circuit using Karnaugh maps. This lab requires knowledge of Karnaugh map simplification which is briefly discussed in the Background & Theory section of this lab handout. ABCO C 0 0 00 0 1 AB 0 0 1 1 0 1 0 0 00 0 1 0 1 1 0 01 0 0 1 0 0 1 1 0 1 1 11 1 0 1 1 0 1 10 1 1 1 1 1 0 Objectives Create minimal logic circuits using Karnaugh map simplification. ✓ Design a minimal seven-segment display decoder. Simulate the circuit in LabVIEW Pre-Lab Preparation For this lab, you will design digital hardware to interface with a seven-segment display module. Read the following manual and note the layout of the segments as well as their assigned pins: http://www.opled.com.tw/ShowProductPDF.aspx?p_id=811 Create a truth table with inputs for a 4-bit binary number and outputs for each of the seven-segments of the display. Fill the output values so the segments will be lit to represent the decimal value of binary input. For example, the row with the binary input equal to 0111 should have a corresponding output row with the A, B, and C segments set to 1 to indicate a decimal value of 7 on the display. Since you are only concerned with single digit decimal values (0-9), mark the remaining unused rows as Don't Cares. Figure 1 - Karnaugh Map Representation of Truth Table After transferring the truth table to a Karnaugh map, cells with common output values, either all Os or all 1s, are grouped into the largest possible rectangles such that the number of cells in the groups is equal to 2² and i is some integer value. Valid cell group arrangements include 4 cells in a line, 2 cells high by 4 cells long, 2 cells by 2 cells, etc. The cells can be used more than once only if it generates the least number of groups. Also, all cells sharing the chosen common output must be contained within a grouping. The groups generated can be converted to a Boolean expression. Each group represents a minimal minterm (1s) or maxterm (Os). The term is minimized by eliminating variables whose non-inverted and inverted forms appear within the same cell group. The terms are then used to derive an SOP or POS expression form of the represented logic function, which may then be converted to a CLC. When choosing the POS form, the variable combination is supposed to equal 0, as is the case when deriving a POS from a truth table. Therefore, the variable's inverse is used when determining a maxterm. Figure 2 illustrates a Karnaugh map translated to minimized SOP and POS expression forms. Notice how cells can also wrap around the map. CD AB 00 01 11 10 Background & Theory Karnaugh Map A Karnaugh map is a handy tool used to derive a minimal Boolean expression from a non-simplified form. Ultimately, the primary use of a Karnaugh map is realizing a minimal Boolean equation. Similar to the number of rows in truth table, a Karnaugh map consists of 2" cells, where n is the number of Boolean input variables. Each cell represents two significant aspects of a Boolean function-a variable combination and its corresponding output value. The cells are formed in a square or rectangle fashion and arranged such that neighboring cells have a single variable difference, otherwise known as Gray code ordering. For simplicity, the input values are placed as column and row labels. A truth table represented as a Karnaugh map is shown in Figure 1. 00 01 11 10 SOP (1's): AC + A'D' + B'D' K-map Color POS (0's): (A+D') (C+D') (A'+B'+C) K-map Color Figure 2 - Karnaugh Map to Minimized SOP and POS Expression Forms Furthermore, an output state level may be a Don't Care which represents a state that is negligible, typically because it will never occur. These cells should only be grouped if the resulting cell group is larger than the group formed without it. In other words, only use Don't Cares if it further simplifies the Boolean express; otherwise, ignore it.