A 7-segment display shows a digit by illuminating a subset of seven segments, labeled a through g:
_a_
f| |b
|_g_|
e| |c
|_d_|Build a decoder that takes a 4-bit BCD digit (0-9) and drives the segment outputs so the display shows the corresponding digit. The output is packed as seg = {g, f, e, d, c, b, a} (bit 0 is segment a, bit 6 is segment g), and a segment is on when its bit is 1.
Interface
| Signal | Direction | Width | Description |
|---|---|---|---|
bcd |
input | 4 | BCD digit, 0-9 (10-15 are invalid / don’t-care) |
seg |
output | 7 | Segment drive, {g,f,e,d,c,b,a}, active-high |
Segment truth table
| bcd | a | b | c | d | e | f | g |
|---|---|---|---|---|---|---|---|
| 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
| 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
| 2 | 1 | 1 | 0 | 1 | 1 | 0 | 1 |
| 3 | 1 | 1 | 1 | 1 | 0 | 0 | 1 |
| 4 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
| 5 | 1 | 0 | 1 | 1 | 0 | 1 | 1 |
| 6 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
| 7 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| 8 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 9 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
Inputs 10-15 never occur in valid BCD, so their output is a don’t-care — driving all segments off is a reasonable default.