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:
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:
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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.
| 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
BCD to 7-Segment Display: Boolean Expressions
The Karnaugh maps will help us define the Boolean Expressions associated with each of the 7 segments.
Karnaugh Map – Segment A
Boolean Expression for Segment A
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.
Booelan Expression for Segment A
Segment A – Logic Gates Diagram
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:
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