An ABCD-to-seven-segment decoder is a combinational circuit that converts a decima digit an appropriate code for the selection of segments in an indicator used to display the decimal digit in a familiar form. The seven outputs of the decoder (a, b, c, d, e, f, g) select the corresponding segments in the display, as shown in Fig (a). The numeric display chosen to represent the decimal digit is shown in Fig (b). Using a truth table and Karnaugh maps, design the BCD-to-seven-segment decoder using a minimum number of gates. The six invalid combinations should result in a blank display. Please note that this is a different design from what we discussed in the lecture. I g d b (a) Segment designation 0123456789 (b) Numerical designation for display 1) Using the truth table, find the sum-of-minterms for the function for each segment.

Database System Concepts
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### ABCD-to-Seven-Segment Decoder

An ABCD-to-seven-segment decoder is a combinational circuit that converts a decimal digit in Binary Coded Decimal (BCD) to an appropriate code for selecting segments in a display indicator. This is used to visually present the decimal digit in an understandable form. The seven outputs of the decoder (segments a, b, c, d, e, f, and g) are responsible for lighting up the corresponding sections in the display, as shown in Figure (a).

- **Figure (a):** Segment Designation
  - This figure illustrates the layout of the seven different segments (a to g) that can be illuminated to form numerals.

- **Figure (b):** Numerical Designation for Display
  - This figure shows the numbers 0 to 9 displayed using the seven segments. Each numeral from 0 to 9 is formed by lighting up a different combination of segments.

Using a truth table and Karnaugh maps, the task is to design the BCD-to-seven-segment decoder with a minimal number of logic gates. Note that there are six invalid combinations; these should result in a blank display.

**Important Note:** This design differs from what was discussed in the lecture.

### Task

1. **Finding the Sum-of-Minterms:**
   - Using the truth table, calculate the sum-of-minterms for the function that controls each segment of the display. This involves determining which combinations of inputs will cause each segment to light up.

This material serves as a guide for understanding the conversion process and the design of digital displays using a BCD-to-seven-segment decoder.
Transcribed Image Text:### ABCD-to-Seven-Segment Decoder An ABCD-to-seven-segment decoder is a combinational circuit that converts a decimal digit in Binary Coded Decimal (BCD) to an appropriate code for selecting segments in a display indicator. This is used to visually present the decimal digit in an understandable form. The seven outputs of the decoder (segments a, b, c, d, e, f, and g) are responsible for lighting up the corresponding sections in the display, as shown in Figure (a). - **Figure (a):** Segment Designation - This figure illustrates the layout of the seven different segments (a to g) that can be illuminated to form numerals. - **Figure (b):** Numerical Designation for Display - This figure shows the numbers 0 to 9 displayed using the seven segments. Each numeral from 0 to 9 is formed by lighting up a different combination of segments. Using a truth table and Karnaugh maps, the task is to design the BCD-to-seven-segment decoder with a minimal number of logic gates. Note that there are six invalid combinations; these should result in a blank display. **Important Note:** This design differs from what was discussed in the lecture. ### Task 1. **Finding the Sum-of-Minterms:** - Using the truth table, calculate the sum-of-minterms for the function that controls each segment of the display. This involves determining which combinations of inputs will cause each segment to light up. This material serves as a guide for understanding the conversion process and the design of digital displays using a BCD-to-seven-segment decoder.
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