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Verilog Tutorial.

BCD addition and Decimal Arithmetic

Refer complete digital basics tutorial

 

In BCD addition of two numbers involve following rules:-

1. Maximum value of the sum for two digits = 9 (max digit 1) + 9 (max digit 2) + 1 (previous addition carry) = 19

2. If sum of two BCD digits is less than or equal to 9 (1001) without carry then the result is a correct BCD number.

3. If sum of two BCD digits is greater than or equal to 10 (1010) the result is in-correct  BCD number. Perform steps 4 for correct BCD sum.

4. Add 6 (0110) to the result.

Examples:- BCD Addition

Add 599 and 984 using BCD numbers

Answer.  Result of BCD addition is 1583

Binary Sum 1, 2 and 3 are greater than 1010.

So, from Step 3 and 4 add ‘6’ to the sum.

BCD Coding and addition examples

Introduction to BCD :-

> BCD stands for Binary Encoded Digital. In BCD every decimal number is represented by four binary bits.

 

> 190 in decimal is equivalent to 0001 1001 0000 in binary encoded decimal

> 0 to 9 in decimal can be represented in binary using four digits and all integers can be represented by these 10 digits.

8
5
3
1
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BCD
1
2
3
599
0101
1001
1001
+984
1001
1000
0100
SUM
1110
10001
1101
carry 1
carry 1
carry 1
Result
1110
10001
1101
+6
0110
0110
0110
End carry 1
0101(5)
1000 (8)
0011 (3)
Digital Logic fundamentals topics @ fcd
Digital basics tutorial
 Binary number discussion, 1 and 2 complement discussion,
Binary arithmetic, Signed Magnitude, overflow, examples
Gray coding, Binary coded digital (BCD) coding, BCD addition
Digital logic gates basic (AND, OR, XOR, NOT) and derived (NAND, NOR and XNOR). Drive XOR from NAND gates. Drive XOR from NOR gates
 Discussion of Boolean Algebra with examples.
Duality Principle, Huntington Postulates, Theorems of Boolean Algebra - discussion with examples, Boolean Functions, Canonical and Standard Forms, Minterms and Maxterms
Sum of Minterms, Product of Maxterms or Canonical Forms,
Karnaugh map or K-map discussion 2, 3, ,4 and 5 var’s
 Prime Implicant and Gate level minimization examples.