design procedure in digital logic circuit

1. DESIGN
PROCEDURE

2. It is the design of combinational circuits starts from the specification
of the problem and culminates in a logic circuit diagram or a set of
Boolean functions from which the logic diagram can be obtained.
WHAT IS A DESIGN PROCEDURE?

3. A conversion circuit must be inserted between the two
system if each uses different codes for the same information.
Thus, a code converter is a circuit that makes the two system
compatible even though each uses a different binary code.
CODE CONVERSION

4. The Excess-3 binary code is an example of a self-
complementary BCD code. A self-complementary
binary code is a code which is always
complimented in itself. By replacing the bit 0 to 1
and 1 to 0 of a number, we find the 1's
complement of the number. The sum of the 1'st
complement and the binary number of a decimal
is equal to the binary number of decimal 9.
BCD to Excess-3 Conversion
Truth table for code-conversion example

5. Maps for BCD and Excess-3 Converter
Each one of the four maps represent one of the four
output of the circuit as a function of the four input
variables. The 1's marked inside the square are
obtained from the minterms that make the output equal
to 1. The 1's are obtained from the truth table by going
over the output columns one at a time. For example, the
column under output z has five 1's; therefore, the map
for z has five 1's each being in a square corresponding
to the minterm that makes z equal to 1.

6. z = D'
y = CD+C'D = CD+ (C+ D)'
x = B'C+B'D+BC'D = B'(C + D) + BC'D'
= B'(C+D)+ B(C + D)'
y = A+BC+ BD = A+ B(C + D)
This manipulation, shown next, illustrates flexibility obtained with multiple-output
systems when implemented with three or more levels of gates;
Boolean function

7. Note that the OR gate whose output is C + D
has been used to implement partially each of
three outputs.
The implementation requires four AND
gates, four OR gates, and one inverter. If
only the normal inputs are available, the first
implementation will require inverters for
variables B, C, and D, and the second
implementation requires invertern for
variables B and D.
Logic Diagram for BCD to Excess-3 Code Converter

8. https://www.javatpoint.com/conversion-of-bcd-to-
excess-3-code-in-digital-electronics
Reference