What is BCD?
BCD, or Binary Coded Decimal, is a representation method for expressing decimal numbers using binary digits. In BCD, each decimal digit is represented by a 4-bit binary code. The four bits can represent values from 0 to 9, equivalent to one decimal digit. BCD is a commonly used method for storing and manipulating decimal numbers in computers and digital systems.
Representation of BCD numbers
In BCD representation, each decimal digit is encoded using 4 bits. The possible binary codes for decimal digits 0 to 9 are as follows:
– 0 is represented as 0000
– 1 is represented as 0001
– 2 is represented as 0010
– 3 is represented as 0011
– 4 is represented as 0100
– 5 is represented as 0101
– 6 is represented as 0110
– 7 is represented as 0111
– 8 is represented as 1000
– 9 is represented as 1001
For example, the decimal number 365 is represented in BCD as follows:
– The digit 3 is represented as 0011
– The digit 6 is represented as 0110
– The digit 5 is represented as 0101
So, 365 in BCD is 0011 0110 0101.
Advantages of BCD representation:
– BCD allows easy conversion between binary and decimal representations.
– When performing arithmetic operations on decimal numbers, BCD can provide accurate results without requiring complex algorithms.
– BCD representation is easier for humans to read and understand compared to pure binary representation.
Internal Processing of BCD in Computers
In computers, BCD numbers are stored and processed using different techniques. One common approach is to store each BCD digit in a separate byte, with 4 bits used to represent the BCD digit and the remaining 4 bits unused. This technique is known as packed BCD.
When performing arithmetic operations on BCD numbers, the computer’s arithmetic logic unit (ALU) typically processes each BCD digit separately, taking care of any carry-over or borrow operations between adjacent digits as required.
It’s important to note that BCD representation requires more storage space compared to pure binary representation, as each BCD digit needs 4 bits, whereas a pure binary digit can be represented with just 1 bit. However, the advantages of BCD in terms of ease of conversion and accuracy in decimal arithmetic make it a valuable representation method for certain applications.
To summarize, BCD is a representation method for expressing decimal numbers using binary digits. It offers advantages in terms of ease of conversion and accuracy in decimal arithmetic. Computers store and process BCD numbers using packed BCD techniques, ensuring accurate results in arithmetic operations.
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