# Explain the function of BCD to a 7-segment Decoder.

**Question**

- a) Explain the function of BCD to a 7-segment Decoder.
- b) Design the Truth table of BCD to 7 Segment Decoder and simplify the circuit by using Karnaugh mapping and Implementing the circuit to segments for a, b, c, and d separately.

**Summary**

A BCD to 7-segment decoder is a circuit that converts a BCD input into a display with seven segments each containing an LED.

To begin, a truth table is built for ten values ranging from 0 to 9, with the segments denoted by the letters a, b, c, d, e, f, and g.

The segment bit for each number will be set to match the number’s form. Except for ‘g,’ all other segments should be ‘0′ s, with g being 1.

Following the creation of the truth table, each segment is given an expression in terms of A, B, C, and D, which are the four bits used to represent 0 to 9 numbers.

Then, using K-map, each expression is solved, and each segment variable has a simpler expression.

**Explanation**

a)

The circuit is on the left, while the display is on the right.

If a number of four bits, A, B, C, and D, is passed to the circuit, the LED display should display that number as seen above.

The values for 5 are 0101 for A, B, C, and D.

The segments a, c, d, f, and g will then be set in the display, while the remaining segments will be unset.

In simple terms, a BCD to 7-segment decoder decodes a number and displays it on an LED display.

**b) **Truth table for BCD to seven segment Decoder:

Lowercase letters a, b, c, d, e, f, and g are used to represent each segment of the seven-segment decoder.

From the truth table above:

There are 1s for 0, 2, 3, 5, 6, 7, 8, and 9 in the segment ‘a’.

As demonstrated below, a Karnaugh map is used to solve each segment function.

The K-map includes 16 entries, of which we know 10 from 0 to 9, and the remaining entries are preserved as ‘X,’ which stands for don’t care, and ‘1′ can be mapped to another ‘1′ or don’t care, resulting in a simplified expression for each segment.

The logical circuit diagram is drawn using the expressions obtained from the K-map:

All of the segments a, b, c, d, e, f, and g have the logic diagram implemented.

Also read, how many bit strings of length 10 contains.