A numeric display that uses 7 seperate LEDs in the shape of a digital '8': Usually a decimal point is tacked on after the 8, just so we can use 8 leads to it:
``` _
|_|
|_|.
```
Also, a display that uses several of these characters.

Commonly found in cheap displays that need to be seen in the dark, such as a car stereo or a burglar alarm.

Name given to LED displays which use 7 segments, each illuminated by one or more LEDs, to represent the numbers 0 to 9 (and more rarely, 0 to 9 and A to F).

The segments are arranged like this:

--
|  |
--
|  |
--

These displays might be more familiar to you as the displays on your clock radio, digital wristwatch, or microwave oven.

When displaying hexadecimal, the letters formed look like this: A b C d E F. 7-segment displays can display _most_ other letters relatively legibly, but have difficulty with letters like W or M. When all the letters need to be displayed legibly, an alpha-numeric or 'starburst' display is used instead.
``` -a-
|   |
f   b
|   |
-g-
|   |
e   c
|   |
-d-

dec BCD 2^  | Output
3 2 1 0 |
W X Y Z | a b c d e f g
------------+--------------
0  0 0 0 0 | 1 1 1 1 1 1 0
1  0 0 0 1 | 0 1 1 0 0 0 0
2  0 0 1 0 | 1 1 0 1 1 0 1
3  0 0 1 1 | 1 1 1 1 0 0 1
4  0 1 0 0 | 0 1 1 0 0 1 1
5  0 1 0 1 | 1 0 1 1 0 1 1
6  0 1 1 0 | 1 0 1 1 1 1 1
7  0 1 1 1 | 1 1 1 0 0 0 0
8  1 0 0 0 | 1 1 1 1 1 1 1
9  1 0 0 1 | 1 1 1 1 0 1 1
A  1 0 1 0 | 1 1 1 0 1 1 1
B  1 0 1 1 | 0 0 1 1 1 1 1
C  1 1 0 0 | 1 0 0 1 1 1 0
D  1 1 0 1 | 0 1 1 1 1 0 1
E  1 1 1 0 | 1 0 0 1 1 1 1
F  1 1 1 1 | 1 0 0 0 1 1 1
```
Yes, it is quite easy to make a little ROM with a few bytes - and frequently that is what is used. Yet, it is also interesting to sit down and work out the logic for the gates that would be necessary to produce such an output.

``` \YZ|  output: a
\ |
WX \| 00   01   11   10
----+----+----+----+----+
00 | 1    0    1    1
|
01 | 0    1    1    1
|
11 | 1    0    1    1
|
10 | 1    1    0    1
|
```
In designing the circuit for the output of 'a', the above Karnaugh map is consulted. There are some patterns in there to simplify the logic necessary. For example: if the bits 'YZ' are 10, then the result is true - no matter what the other values are.

Form this point on, the capital input refers to a '1', and lower case input refers to a '0'. Thus - 'YZ' is '11' and 'Yz' is 10. Furthermore, the logical 'or' is represented by '+' and logical 'and' is represented by multiplication. Just as with math notation 'x*y' can be written as 'xy', so it can be here too.

The output for 'a' begins with:
Yz
Squares are also useful, and realize that they can wrap around the edges. The square: Wz also covers some in the lower half wrapping around the edge.
Yz + Wz
The other squares that exist are: Yw and XY. Although it almost escaped me, there is another square too: 'zx'. This one is the four outermost corners.
Yz + Wz + Yw + XY + zx

There are some stragglers that are not possible to get into a square or run of 4. Three inputs are necessary to cover them. The fewer inputs the better. These are the locations at yZwX and yZWx. By pairing them with an adjacent '1' one of the inputs can be removed.

a = Yz + Wz + Yw + XY + xz + ZwX + WXy

Segment 'a' is to be lit up if any of the following is true:
• Y is true and Z is false.
• W is true and Z is false.
• Y is true and W is false.
• X is true and Y is true.
• Z is true, W is false, and X is true.
• W is true, X is true, and Y is false.

From this point onward, it is left as an exercise to the reader as it would be a waste of nodegell to go through an extensive explanation of the logic behind the remaining 6 outputs of the BCD to 7 Segment integrated circuit. Following the above method of identifying the largest sets of adjacent '1's should make the simplest possible circuit necessary.

This node has been brought to you by Node Your Homework - the above problem was an assignment for ECE 352 - a class I took in 1992.