Name _________________________

Karnaugh Map and Circuit Design Problem
Due Saturday, April 1 (25 pts.)

Consider the 7-segment display (now nearly extinct):

Seven segment LED display

Display of 0 through 9 with a seven segment display

In the following, assume that a 7-segment display is to display one of the digits from 0 to 9. The goal is to design a circuit whose input is the binary representation of that digit (0-9) and whose output is the state of the segments of the seven-segment display. Represent an "ON" segment (the filled pieces in the image above) with a logical true or "1" . Represent an "OFF" segment with a false or "0" .

Create a truth table for this switching function that maps four bits to seven bits. The four bits of input represent the binary encoding of a single decimal digit (for example, 0 = "0000" and 9 = "1001"). The seven bits of output indicate which if the seven segments of the display are switched on. Note that of the 16 possible 4-bit inputs, you only care about the outputs for 10 of them (0-9).

Give a Karnaugh map (with don't cares) for each of the switching functions. Write the simplified sum-of-products form of each, taking advantage of "don't cares."

s0:                                                  s1: 

                                         

s2:                                                  s3: 

                                         

s4:                                                  s5: 

                                         

s6: 

Construct the logic circuit that outputs the state of the last segment (s6) in the seven-segment display, given the four bits of input (x, y, z, and w).