In order to display numbers 0 to 9 we use the 7 segment display, those are 7 straight light emitting diodes or anodes denoted by the letters a through g. each segment can be lighted up with the circuit of 7 segment decoder.

Decimal seven-segment decoder truth table

Inputs				Number	Display segment							Segments numbering sequences
D	C	B	A		a	b	c	d	e	f	g
0	0	0	0	0	1	1	1	1	1	1	0
0	0	0	1	1	0	1	1	0	0	0	0
0	0	1	0	2	1	1	0	1	1	0	1
0	0	1	1	3	1	1	1	1	0	0	1
0	1	0	0	4	0	1	1	0	0	1	1
0	1	0	1	5	1	0	1	1	0	1	1
0	1	1	0	6	1	0	1	1	1	1	1
0	1	1	1	7	1	1	1	0	0	0	0
1	0	0	0	8	1	1	1	1	1	1	1
1	0	0	1	9	1	1	1	1	0	1	1
All other combinations don't care					X	X	X	X	X	X	X

For any decimal number we can see the state of each segment, when 1 means that the segment is on (illuminated) and 0 is off.

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Segment:

Seven segment (0 to 9 decimal) decoder circuit

To present all hex characters, we must modify the gates circuits to represent the additional characters A, b, C, d, E and F, and to display the corresponding states of the segments. We can see the new truth table values, in the next table.

Seven-segment Hex decoder truth table

Inputs				Decimal number	Display segment							Segments numbering sequences
A	B	C	D		a	b	c	d	e	f	g
0	0	0	0	0	1	1	1	1	1	1	0
0	0	0	1	1	0	1	1	0	0	0	0
0	0	1	0	2	1	1	0	1	1	0	1
0	0	1	1	3	1	1	1	1	0	0	1
0	1	0	0	4	0	1	1	0	0	1	1
0	1	0	1	5	1	0	1	1	0	1	1
0	1	1	0	6	1	0	1	1	1	1	1
0	1	1	1	7	1	1	1	0	0	0	0
1	0	0	0	8	1	1	1	1	1	1	1
1	0	0	1	9	1	1	1	1	0	1	1
1	0	1	0	A	1	1	1	0	1	1	1
1	0	1	1	b	0	0	1	1	1	1	1
1	1	0	0	C	1	0	0	1	1	1	0
1	1	0	1	d	0	1	1	1	1	0	1
1	1	1	0	E	1	0	0	1	1	1	1
1	1	1	1	F	1	0	0	0	1	1	1

K-map for segment − a

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Segment:

Seven-segment containing all segments - Hex decoder circuit