# Binary-Coded Decimal Or BCD

#### Contents

## Definition

BCDorbinary-coded decimalis a special kind of representation of a decimal number in binary numbers. In binary-coded decimal each individual digit of a number is converted into a binary number, and then by combining them all, the BCD code is generated. But always remember that a binary-coded decimal is not a binary representation of a decimal number.

## Examples

The

BCDorbinary-coded decimalof the number15is 00010101. The 0001 is the binary code of 1 and 0101 is the binary code of 5.

Any single decimal numeral [0-9] can be represented by a four bit pattern. The procedure of encoding digits is called **"Natural BCD" (NBCD)**, where each decimal digit is represented by its corresponding four-bit binary value.

## Types

Generally there are 2 types of BCD: unpacked and packed.

Unpacked BCD:In the case of unpacked BCD numbers, each four-bit BCD group corresponding to a decimal digit is stored in a separate register inside the machine. In such a case, if the registers are eight bits or wider, the register space is wasted.

Packed BCD:In the case of packed BCD numbers, two BCD digits are stored in a single eight-bit register. The process of combining two BCD digits so that they are stored in one eight-bit register involves shifting the number in the upper register to the left 4 times and then adding the numbers in the upper and lower registers.

There is the another one which is not really considered as BCD:

Invalid BCD:There are some numbers are not considered as BCD. They are 1010, 1011, 1100, 1101, 1110, 1111.

## Differences Between BCD And Simple Binary Representation

In simple binary representation of any number we just convert the whole number into its binary form by repeteadly dividing 2 again and again. But in the case of BCD, we need not to do this. If anyone knows the binary representation of the numbers 0 to 9, he/she can make a BCD code of any number because, in BCD, we just convert each individual digit of any number to binary and then write them together.

In the case of **946**, the **binary representation** of this number is 01110110010. Here we convert the total number into its binary form. But when we form the **BCD** code of the number 946, that'll be

$9 = 1001, 4 = 0100, 6 = 0110 \Rightarrow 100101000110.$

## Use Of Binary-Coded Decimal

The use of BCD can be summarized as follows:

- BCD takes more space and more time than standard binary arithmetic.
- It is used extensively in applications that deal with currency because floating point representations are inherently inexact.
- Database management systems offer a variety of numeric storage options; “Decimal” means that numbers are stored internally either as BCD or as fixed-point integers
- BCD offers a relatively easy way to get around size limitations on integer arithmetic.

## How many bits would be required to encode decimal numbers 0 to 9999 in straight binary and BCD codes? What would be the BCD equivalent of decimal 27 in 16-bit representation?

- Total number of decimals to be represented=10 000=104 = 213 29.
- Therefore, the number of bits required for straight binary encoding = 14.
- The number of bits required for BCD encoding = 16.
- The BCD equivalent of 27 in 16-bit representation =
0000000000100111.

Find a decimal number which can be represented with 1's only and no 0's in binary, and takes 4 bits in binary. In other words, if you convert that decimal number into binary, it cannot be like 10101 which does contain 0's. It should only contain a certain number of 1's.

Submit your answer as the sum of digits of the **binary-coded decimal** of that decimal number.

For binary-coded decimal, read the wiki Binary-Coded Decimal.

**Cite as:**Binary-Coded Decimal Or BCD.

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