What does the basic description of a digital Decoder as a minterm output generator mean?
The correct answer and explanation is:
Correct Answer:
A digital decoder as a minterm output generator means that the decoder generates output lines that correspond to the minterms of its input variables.
Explanation:
A digital decoder is a combinational logic circuit that takes n input lines and activates exactly one of its 2^n output lines based on the binary value of the inputs. For example, a 3-to-8 decoder has 3 inputs and 8 outputs. Only one output line will be active (usually logic high or low depending on design) for each combination of input values.
The concept of a minterm comes from Boolean algebra. A minterm is a unique combination of input variables where each variable appears once, either in true or complemented form. In terms of truth tables, each minterm corresponds to exactly one row where the output is 1. For instance, for inputs A and B:
- A’B’ is minterm 0
- A’B is minterm 1
- AB’ is minterm 2
- AB is minterm 3
When a decoder is described as a minterm generator, it means that each output of the decoder represents one of these unique combinations of inputs. Therefore, for a 2-to-4 decoder:
- If inputs are 00, output 0 (A’B’) is active
- If inputs are 01, output 1 (A’B) is active
- If inputs are 10, output 2 (AB’) is active
- If inputs are 11, output 3 (AB) is active
This makes the decoder an essential tool in digital logic design for selecting one specific line out of many, implementing logic functions using sum-of-minterms, and building memory address decoding circuits. It is especially useful in programmable logic devices, control units, and microprocessor instruction decoding.