Combination Circuit Design
- Design of a combinational circuit is the development of a circuit from a description
of its function.
– “design an excess-123 encoder”
– “provide a circuit that will multiplex one of three
8-bit input buses onto an 8-bit output bus.”
Design Procedure
1. Determine the required number of inputs and outputs and
assign variables to them.
2. Derive the truth table that defines the required
relationship between inputs and outputs.
3. Obtain and simplify the Boolean function.
4. Draw the logic diagram.
5. Verify the correctness of the design.
Code Converter Example
- Design a circuit that converts a binary-coded decimal (BCD) codeword to its corresponding excess-3 codeword.
- If the input is a number n expressed in BCD, the output should be the number n+3 expressed in binary.
- We need 4 input variables (a,b,c,d) and 4 output functions w(a,b,c,d),x(a,b,c,d),y(a,b,c,d),z(a,b,c,d)).
By convention, a and w are the most significant bits of
the input and output, respectively.
- The truth table relating the input and output variables is shown at right.
- Note that the outputs for inputs 1010 through 1111 are don't cares.
The K-maps for w( ), x( ), y( ), and z( ) can be
constructed with don't cares.The simplified Boolean functions derived from the
K-maps are:
– z = d’
– y = cd + c’d’
– x = b’c + b’d + bc’d’
– w = a+bc+bd
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