Digital Electronics: Binary-Coded-Decimal to Seven-Segment Decoder

[GTdan]

This is one of the problems I have for homework:

Consider a BCD-to-seven-segment decoder and suppose that the BCD data are represented by the logic variables B8, B4, B2, and B1. For example, the decimal number 7 is represented in BCD by the word 0111 in which the leftmost bit is B8=0, the second bit is B4=1, and so forth. a: Find a logic circuit based on the product of maxterms having output A that is high only if segment A of the display is to be on. b: Repeat for segment B.

Here is my problem- I have no idea what the question is asking me for. The words "circuit based on the product of maxterms" confuses me and I just don't know what to look for. I am 100% sure if I knew what it was asking, I could do the problem but it doesn't say anything like that in the section explaining these decoders. Any help would be appreciated. Thanks in advance :)

 

[GTdan]

for anyone who may have been trying. Don't worry about it anymore and thanks. I finally figured it out. :)

 

[wais]

A binary-coded-decimal (BCD) to seven-segment decoder is a digital circuit that converts a binary-coded decimal input into a seven-segment display output. This type of decoder is commonly used in electronic devices such as calculators, digital clocks, and other display systems.

In this particular problem, you are given four input variables B8, B4, B2, and B1 representing the BCD data. Your task is to design a logic circuit that will produce an output signal A, which will turn on segment A of the seven-segment display, based on the input BCD data.

To solve this problem, you need to understand the concept of maxterms and product of maxterms. In Boolean algebra, a maxterm is a logical expression that is equal to 1 when all of its inputs are equal to 0. A product of maxterms is a logical expression that is equal to 1 only when a specific combination of inputs is equal to 0.

Now, let's break down the problem into two parts:

a) Find a logic circuit based on the product of maxterms having output A that is high only if segment A of the display is to be on.

To solve this part, you need to first identify the truth table for the BCD-to-seven-segment decoder. The truth table for this decoder will have 16 rows, representing all the possible combinations of the BCD inputs (B8, B4, B2, B1) and seven columns representing the seven segments (A, B, C, D, E, F, G) of the seven-segment display.

For this problem, we are only interested in segment A, so we can ignore the other six columns. Now, look at the truth table and find the rows where segment A is equal to 1 (on). In this case, it will be rows 1, 3, 4, 5, 7, 9, 12, 13, 15.

Next, we need to convert these rows into logical expressions using maxterms. For example, row 1 can be represented as A = B8'B4B2B1. Similarly, row 3 can be represented as A = B8B4'B2B1. Continue this process for all the rows where segment A is equal to 1.

Finally, combine all these logical expressions using the logical OR operation to get the final expression for output A.