Decimal or BCD Adder | Digital Circuits - Electronics and Communication Engineering (ECE) PDF Download

Definition

Note: The decimal number requires 4 bits to represent in the BCD code, and the circuit must have an input carry and an output carry.

There is the following table used in designing of BCD-Adder.From the above table, it is clear that if the produced sum is between 1 to 9, the Binary and the BCD code is the same. But for 10 to 19 decimal numbers, both the codes are different. In the above table, the binary sum combinations from 10 to 19 give invalid BCD. There are the following points that help the circuit to identify the invalid BCD.

• It is obvious from the table that a correction is needed when the 'Binary Sum' has an output carry K=1.
• The other six combinations from 10 to 15 need correction in which the bit on the Z₈ position is 1.
• In the Binary sum of 8 and 9, the bit on the Z₈ position is also 1. So, the second step fails, and we need to modify it.
• To distinguish these two numbers, we specify that the bit on the Z₄ or Z₂ position also needs to be 1 with the bit of Z₈
• The condition for a correction and an output carry can be expressed by the Boolean function:
  

Once the circuit found the invalid BCD, the circuit adds the binary number of 6 into the invalid BCD code to make it valid.

In the above diagram,

• We take a 4-bit Binary-Adder, which takes addend and augend bits as an input with an input carry 'Carry in'.
• The Binary-Adder produces five outputs, i.e., Z₈, Z₄, Z₂, Z₁, and an output carry K.
• With the help of the output carry K and Z₈, Z₄, Z₂, Z₁ outputs, the logical circuit is designed to identify the Cout
• The Z₈, Z₄, Z₂, and Z₁ outputs of the binary adder are passed into the 2nd 4-bit binary adder as an Augend.
• The addend bit of the 2nd 4-bit binary adder is designed in such a way that the 1st and the 4^th bit of the addend number are 0 and the 2^nd and the 3^rd bit are the same as C_out. When the value of Cout is 0, the addend number will be 0000, which produce the same result as the 1^st 4-bit binary number. But when the value of the C_out is 1, the addend bit will be 0110, i.e., 6, which adds with the augent to get the valid BCD number.

Example: 1001 + 1000

1. First, add both the numbers using a 4-bit binary adder and pass the input carry to 0.
2. The binary adder produced the result 0001 and carried output 'K' 1.
3. Then, find the C_out value to identify that the produced BCD is invalid or valid using the expression C_out=K+Z₈.Z₄+Z₈.Z₂.
   K = 1
   Z₈ = 0
   Z₄ = 0
   Z₂ = 0
   C_out = 1+0*0+0*0
   C_out = 1+0+0
   C_out = 1
4. The value of C_out is 1, which expresses that the produced BCD code is invalid. Then, add the output of the 1^st 4-bit binary adder with 0110.
   = 0001+0110
   = 0111
5. The BCD is represented by the carry output as:
   BCD=C_out Z₈ Z₄ Z₂ Z₁=1 0 1 1 1