DISPLAY 7 SEGMENT

   7-Segment Displays
Truth Table to Decode Binary into 7-Segment

Decimal Number		Inputs					Outputs
		D	C	B	A		a	b	c	d	e	f	g
0 1 2 3 45 6 7 8 9		0 0 0 0 00 0 0 1 1	0 0 0 0 11 1 1 0 0	0 0 1 1 00 1 1 0 0	0 1 0 1 01 0 1 0 1		1 0 1 1 01 1 1 1 1	1 1 1 1 10 0 1 1 1	1 1 0 1 11 1 1 1 1	1 0 1 1 01 1 0 1 1	1 0 1 0 00 1 0 1 0	1 0 0 0 11 1 0 1 1	0 0 1 1 11 1 0 1 1

 


Karnaugh Mapping for Segment a:
The Truth Table:

	BA	00	01	11	10
DC\
00		1	0	1	1
01		0	1	1	1
11		x	x	x	x
10		1	1	x	x

Boxing ones:

	BA	00	01	11	10
DC\
00		1	0	1	1
01		0	1	1	1
11		x	x	x	x
10		1	1	x	x

Red cells are represented by B; this is a 4x2 supercell.

	BA	00	01	11	10
DC\
00		1	0	1	1
01		0	1	1	1
11		x	x	x	x
10		1	1	x	x

Green cells are represented by D; this is a 2x4 supercell.
So far then we have:

	BA	00	01	11	10
DC\
00		1	0	1	1
01		0	1	1	1
11		x	x	x	x
10		1	1	x	x

where grey boxes indicate cells included in more that one supercell. The shaded boxes are represented by B+D.
Focusing on the remaining cells with ones:

	BA	00	01	11	10
DC\
00		1	0	1	1
01		0	1	1	1
11		x	x	x	x
10		1	1	x	x

Blue cells are represented by A^.C; this is a 2x2 supercell.

	BA	00	01	11	10
DC\
00		1	0	1	1
01		0	1	1	1
11		x	x	x	x
10		1	1	x	x

Cyan cells are represented by A'^.C'; this is a 2x2 wrap-around supercell.

	BA	00	01	11	10
DC\
00		1	0	1	1
01		0	1	1	1
11		x	x	x	x
10		1	1	x	x

All cells are represented by B + D + A^.C + A'^.C', as shown for segment a.
Karnaugh Mapping for Segment c:
The Truth Table:

	BA	00	01	11	10
DC\
00		1	1	1	0
01		1	1	1	1
11		x	x	x	x
10		1	1	x	x

Boxing zeroes:

	BA	00	01	11	10
DC\
00		1	1	1	0
01		1	1	1	1
11		x	x	x	x
10		1	1	x	x

The red cells are represented by C'^.B^.A'; of course the complement is required for the final realization. Thus (C'^.B^.A')' is the combination of gates that is realized from the Karnaugh mapping of zeroes. Application of De Morgan's theorem results in the combination of gates shown for segment c:
(C'^.B^.A')' = C + B' + A

   Decoder for segment a

D C B A a 0 1 2 3 45 6 7 8 9 0 0 0 0 00 0 0 1 1 0 0 0 0 11 1 1 0 0 0 0 1 1 00 1 1 0 0 0 1 0 1 01 0 1 0 1 1 0 1 1 01 1 1 1 1

   Decoder for segment b

		D	C	B	A		b
0 1 2 3 45 6 7 8 9		0 0 0 0 00 0 0 1 1	0 0 0 0 11 1 1 0 0	0 0 1 1 00 1 1 0 0	0 1 0 1 01 0 1 0 1		1 1 1 1 10 0 1 1 1

   Decoder for segment c

D C B A c 0 1 2 3 45 6 7 8 9 0 0 0 0 00 0 0 1 1 0 0 0 0 11 1 1 0 0 0 0 1 1 00 1 1 0 0 0 1 0 1 01 0 1 0 1 1 1 0 1 11 1 1 1 1

BA  00   01   11   10  DC\  00  1 1 1 0  01  1 1 1 1  11  x x x x  10  1 1 x x Karnaugh

   Decoder for segment d

D C B A d 0 1 2 3 45 6 7 8 9 0 0 0 0 00 0 0 1 1 0 0 0 0 11 1 1 0 0 0 0 1 1 00 1 1 0 0 0 1 0 1 01 0 1 0 1 1 0 1 1 01 1 0 1 1

   Decoder for segment e

		D	C	B	A		e
0 1 2 3 45 6 7 8 9		0 0 0 0 00 0 0 1 1	0 0 0 0 11 1 1 0 0	0 0 1 1 00 1 1 0 0	0 1 0 1 01 0 1 0 1		1 0 1 0 00 1 0 1

	BA	00	01	11	10
DC\
00		1	0	0	1
01		0	0	0	1
11		x	x	x	x
10		1	0	x	x

 

   Decoder for segment f

		D	C	B	A		f
0 1 2 3 45 6 7 8 9		0 0 0 0 00 0 0 1 1	0 0 0 0 11 1 1 0 0	0 0 1 1 00 1 1 0 0	0 1 0 1 01 0 1 0 1		1 0 0 0 11 1 0 1 1      Decoder for segment g D C B A g 0 1 2 3 45 6 7 8 9 0 0 0 0 00 0 0 1 1 0 0 0 0 11 1 1 0 0 0 0 1 1 00 1 1 0 0 0 1 0 1 01 0 1 0 1 0 0 1 1 11 1 0 1 1