7-Segment Display

Interactive BCD to seven-segment decoder — toggle bits or pick a digit to see segment logic.

Display

BCD Input

Segment Status

Digit 0 → BCD 0000 → Segments: a, b, c, d, e, f

Segment Logic Equations (Σ minterms)

a= Σm(0, 2, 3, 5, 6, 7, 8, 9)1

b= Σm(0, 1, 2, 3, 4, 7, 8, 9)1

c= Σm(0, 1, 3, 4, 5, 6, 7, 8, 9)1

d= Σm(0, 2, 3, 5, 6, 8, 9)1

e= Σm(0, 2, 6, 8)1

f= Σm(0, 4, 5, 6, 8, 9)1

g= Σm(2, 3, 4, 5, 6, 8, 9)0

Full SOP Boolean Equations

a=D3′D2′D1′D0′ + D3′D2′D1D0′ + D3′D2′D1D0 + D3′D2D1′D0 + D3′D2D1D0′ + D3′D2D1D0 + D3D2′D1′D0′ + D3D2′D1′D0

b=D3′D2′D1′D0′ + D3′D2′D1′D0 + D3′D2′D1D0′ + D3′D2′D1D0 + D3′D2D1′D0′ + D3′D2D1D0 + D3D2′D1′D0′ + D3D2′D1′D0

c=D3′D2′D1′D0′ + D3′D2′D1′D0 + D3′D2′D1D0 + D3′D2D1′D0′ + D3′D2D1′D0 + D3′D2D1D0′ + D3′D2D1D0 + D3D2′D1′D0′ + D3D2′D1′D0

d=D3′D2′D1′D0′ + D3′D2′D1D0′ + D3′D2′D1D0 + D3′D2D1′D0 + D3′D2D1D0′ + D3D2′D1′D0′ + D3D2′D1′D0

e=D3′D2′D1′D0′ + D3′D2′D1D0′ + D3′D2D1D0′ + D3D2′D1′D0′

f=D3′D2′D1′D0′ + D3′D2D1′D0′ + D3′D2D1′D0 + D3′D2D1D0′ + D3D2′D1′D0′ + D3D2′D1′D0

g=D3′D2′D1D0′ + D3′D2′D1D0 + D3′D2D1′D0′ + D3′D2D1′D0 + D3′D2D1D0′ + D3D2′D1′D0′ + D3D2′D1′D0

BCD to 7-Segment Truth Table

Digit	D3	D2	D1	D0	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

About the 7-Segment Display

A seven-segment display uses 7 individually controlled segments (a–g) to represent decimal digits 0–9. A BCD-to-7-segment decoder takes a 4-bit binary-coded decimal (BCD) input and activates the appropriate segments. Each segment can be expressed as a sum-of-minterms logic function of the 4 BCD input bits. These decoders are used in clocks, calculators, digital meters, and any display needing human-readable numeric output.

Digit	D3	D2	D1	D0	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

Digit	D3	D2	D1	D0	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

Digit	D3	D2	D1	D0	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