BCD to 7-Segment Display

Posted on September 7, 2018 by Administrator Posted in A Level Concepts, Computer Hardware, Computer Science, Computing Concepts, Physical Computing

What is BCD code?

In computing and electronic systems, binary-coded decimal (BCD) is used to encode decimal numbers (base-10 numbers) in a binary form where each decimal digit is represented by a nibble (4 bits).

For instance decimal number 5 is represented as 0101 in BCD as 5 = 4 + 1

8	4	2	1
0	1	0	1

The 10 digits in BCD:

Decimal Digit	BCD Nibble
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001

Numbers larger than 9, having two or more digits in the decimal system, are expressed one digit at a time using on nibble per digit. For example, the decimal number 365 is encoded as:

0011 0110 0101

7-Segment Display

A lot of electronic devices use 7-segment displays (Watch, alarm clock, calculator etc.).
Typically 7-segment displays consist of seven individual coloured LED’s (called the segments). Each segment can be turned on or off to create a unique pattern/combination. Each segment is identified using a letter between A to G as follows:

The 10 descimal digits can be displayed on a seven-segment display as follows:

BCD to 7-Segment Display: Truth Tables & Karnaugh Maps

We will use four inputs A,B,C and D to represent the four BCD digits as ABCD (A is the most significant digit, D is the least significant digit). When creating an electronic circuit we could use 4 switches to represent these 4 inputs.

We will need 7 outputs one for each segment. So let’s investigate each segment one at a time.

Segment ABCDEFG

Segment A should be on for the following values:

BCD: 0000	BCD: 0010	BCD: 0011	BCD: 0101
BCD: 0110	BCD: 0111	BCD: 1000	BCD: 1001

Segment A should be off for the following values:

BCD: 0001

BCD: 0100

Segment A should also be off for the following BCD values which are not used to represent decimal digits values from 0 to 9:

1010
1011
1100
1101
1110
1111

Note that these values could be used to represent hexadecimal values A to F (10 to 15). Here we will not display anything instead.

Hence the Truth Table for Segment A is as follows:

Inputs				Output
A	B	C	D	Segment A
0	0	0	0	1
0	0	0	1	0
0	0	1	0	1
0	0	1	1	1
0	1	0	0	0
0	1	0	1	1
0	1	1	0	1
0	1	1	1	1
1	0	0	0	1
1	0	0	1	1
1	0	1	0	0
1	0	1	1	0
1	1	0	0	0
1	1	0	1	0
1	1	1	0	0
1	1	1	1	0

This Truth table can be represented using a Karnaugh Map:

Karnaugh Map for Segment A

Follow the same process to define the Truth Table and Karnaugh Map of the B segment:

Follow the same process to define the Truth Table and Karnaugh Map of the C segment:

Follow the same process to define the Truth Table and Karnaugh Map of the D segment:

Follow the same process to define the Truth Table and Karnaugh Map of the E segment:

Follow the same process to define the Truth Table and Karnaugh Map of the F segment:

Follow the same process to define the Truth Table and Karnaugh Map of the G segment:

BCD to 7-Segment Display: Boolean Expressions

The Karnaugh maps will help us define the Boolean Expressions associated with each of the 7 segments.

Segment ABCDEFG

Karnaugh Map:

Karnaugh Map – Segment A

Boolean Expression:

Boolean Expression for Segment A

Use the Karnaugh Map for the B segment to define the Boolean Expression of the B segment.

Use the Karnaugh Map for the C segment to define the Boolean Expression of the C segment.

Use the Karnaugh Map for the D segment to define the Boolean Expression of the D segment.

Use the Karnaugh Map for the E segment to define the Boolean Expression of the E segment.

Use the Karnaugh Map for the F segment to define the Boolean Expression of the F segment.

Use the Karnaugh Map for the G segment to define the Boolean Expression of the G segment.

BCD to 7-Segment Display: Logic Gates Diagrams

We can now convert each Boolean expression into a Logic Gates circuit to link our 4 inputs (switches) to our 7-segment display using a range of logic gates.

Segment ABCDEFG

Boolean Expression:

Booelan Expression for Segment A

Logic Gates Diagram:

Segment A – Logic Gates Diagram

Use the Boolean Expression of the B segment to draw the logic gates diagram required to control the LED of the B segment.

Use the Boolean Expression of the C segment to draw the logic gates diagram required to control the LED of the C segment.

Use the Boolean Expression of the D segment to draw the logic gates diagram required to control the LED of the D segment.

Use the Boolean Expression of the E segment to draw the logic gates diagram required to control the LED of the E segment.

Use the Boolean Expression of the F segment to draw the logic gates diagram required to control the LED of the F segment.

Use the Boolean Expression of the G segment to draw the logic gates diagram required to control the LED of the G segment.

Testing

You can now recreate your logic gates circuit using logic.ly to test if it behaves as expected for all 16 BCD entries.
e.g. For Segment A:

Logic Gates Circuit for Segment A

BCD to 7-Segment Display Integrated Circuit

All these 7 logic gates diagrams can all be integrated into one single integrated circuit: The CD74HCT4511E is a CMOS logic high-speed BCD to 7-segment Latch/Decoder/Driver with four inputs and is used to use these 4 inputs (BCD nibble) to control the display of a 7-segment display.

Hex/BCD to 7-Segment Display Integrated Circuit

A very similar approach can be used to display hexadecimal digits as these are also based on a nibble per digit.

The extra values that we discarded previously (BCD: 1010, 1011, 1100, 1101, 1110, 1111) can be used to represent the extra 6 digits available in hexadecimal: