Binary coded decimal facts for kids

Binary coded decimal (often called BCD) is a special way that computers and other digital devices can store and work with numbers. Imagine you have a regular number like 25. In BCD, instead of converting the whole number 25 into binary (which would be 11001), you convert each digit separately.

So, for the number 25:

• The digit '2' becomes `0010` in binary.
• The digit '5' becomes `0101` in binary.

When you put them together, the BCD representation of 25 is `0010 0101`. This makes it easier for computers to show numbers on displays, like on a calculator or a digital clock, because each group of four binary bits directly represents one decimal digit.

What is Binary Coded Decimal?

Binary Coded Decimal, or BCD, is a system where each digit from 0 to 9 is represented by its own four-bit binary code. This is different from how computers usually store numbers, where a whole number is converted into one long binary sequence.

How BCD Works

In BCD, every single decimal digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) gets its own unique 4-bit binary code.

• 0 is `0000`
• 1 is `0001`
• 2 is `0010`
• 3 is `0011`
• 4 is `0100`
• 5 is `0101`
• 6 is `0110`
• 7 is `0111`
• 8 is `1000`
• 9 is `1001`

Why Use BCD?

BCD is very useful when you need to display numbers accurately, especially in devices that show decimal numbers. Think about digital clocks, calculators, or even some older cash registers. When a computer uses BCD, it's simpler to convert the binary code back into a decimal digit for display. This avoids complicated calculations that would be needed if the whole number was stored as a single binary value.

For example, if a calculator needs to show the number 7, it just looks at the 4-bit BCD code `0111` and knows to display a '7'. If it were a regular binary number, it would have to convert the entire binary value of, say, 700, back into decimal before showing it.

BCD vs. Pure Binary

The main difference between BCD and pure binary is how they handle numbers.

• Pure Binary: Converts the entire number into one binary sequence. For example, 12 in pure binary is `1100`.
• BCD: Converts each digit separately. For 12, the '1' is `0001` and the '2' is `0010`. So, 12 in BCD is `0001 0010`.

Pure binary is more efficient for storage and calculations inside a computer's processor. BCD is often better for input/output operations, like reading numbers from a keypad or showing them on a screen.

Where is BCD Used?

BCD is still used in many places, especially where exact decimal representation is important.

• Digital Clocks: To display the time accurately.
• Calculators: To show the numbers you type and the results of calculations.
• Financial Systems: In some older systems, BCD was used to avoid rounding errors that can happen when converting decimal numbers to pure binary and back. This is very important for money calculations.
• Embedded Systems: Small computer systems in devices often use BCD for simple displays.

See also

In Spanish: Decimal codificado en binario para niños