This document discusses binary coded decimal (BCD). It defines BCD as a numerical code that assigns a 4-bit binary code to each decimal digit from 0 to 9. Numbers larger than 9 are expressed digit by digit in BCD. BCD is used because it is easy to encode/decode decimals and useful for digital systems that display decimal outputs. The document also describes how addition and subtraction are performed in BCD through binary addition rules and handling carries.

1. BCD
1. Introduction to BCD.
2. Defination of BCD.
3. How to express Digit in BCD
4. Why BCD is used??
5. Addition in BCD..... :D
6. Subtraction in BCD....... :)

2. DLD Presentation..

3. History
In the 1972 case Gottschalk v. Benson, the U.S. Supreme Court overturned
a lower court decision which had allowed a patent for converting BCD
encoded numbers to binary on a computer. This was an important case in
determining the patentability of software and algorithms.
Application [USE OF BCD....]
The BIOS in many personal computers stores the date and time in BCD
because the MC6818 real-time clock chip used in the original IBM PC AT
motherboard provided the time encoded in BCD. This form is easily
converted into ASCII for display.[18]
The Atari 8-bit family of computers used BCD to implement floating-point
algorithms. The MOS 6502 processor has a BCD mode that affects the
addition and subtraction instructions.

4. Defination of BCD..Binary Coded
Decimal
Binary coded decimal (BCD) is a system of writing numbers that
assigns a four-digit binary code to each digit 0 through 9 in a
decimal (base-10) numeral. The four-bit BCD code for any
particular single base-10 digit is its representation in binary
notation, as follows:
0 = 0000
1 = 0001
2 = 0010
3 = 0011
4 = 0100
5 = 0101
6 = 0110

5.  7 = 0111
 8 = 1000
 9 = 1001
Numbers larger than 9, having two or more digits in the decimal
system, are expressed digit by digit. For example, the BCD
rendition of the base-10 number 1895 is
1 8 9 5
0001 1000 1001 0101

6. Why BCD is Used...
1. It is easy to encode and decode decimals into BCD
and vice versa. • It is also simple to implement a
hardware algorithm for the BCD converter.
2. It is very useful in digital systems whenever decimal
information is given eitheras inputs or displayed as
outputs.
3. Digital voltmeters, frequency converters and digital
clocks all use BCD as they display output information
in decimal

7. BCD Addition
BCD is a numerical code which has several rules for
addition. The rules are given below in three steps with an
example to make the idea of BCD Addition clear.
1.At first the given number are to be added using the rule of
binary. For example

8. BCD Addition.
If the four bit result of addition is greater than 9 and if a carry bit is
present in the result then it is invalid and we have to add 6 whose binary
equivalent is (0110)2 to the result of addition. Then the resultant that we
would get will be a valid binary coded number. In case 1 the result was
(1111)2 which is greater than 9 so we have to add 6 or (0110)2 to it.

9. BCD Substraction
• At first 1’s compliment of the subtrahend is done, which is 1101 1110 1001
and is added to 0101 0100 0001. This step is called adder 1.
• Now after addition if any carry occurs then it will be added to the next group
of numbers towards MSB. Then EAC will be examined. Here, EAC = 1. So
the result of addition is positive and true result of adder 1 will be transferred to
adder 2.
• Now notice from LSB. There are three groups of four bit numbers. 1010 is
added 1011 which is the first group of numbers because it do not have any
carry. The result of the addition is the final answer.
• Carry 1 will be ignored as it is from the rule.
• Now move to the next group of numbers. 0000 is added to 0010 and gives the
result 0010. It is the final result again.
• Now again move to the next group here 0000 is also added to 0011 to give the
final result 0011.