Combinational Logic

What is the difference between Combinational circuits and Sequential circuits?

- Standards to divide

1) Existence of State

2) Existence of Storage element(=memory)

- Both Combinational circuits and Sequential circuits are kinds of Digital logic circuit

 

- Combinational Circuits: output = function(input 'only') --> 입력에 의해 출력이 정해짐. 입력만 알면 출력은 정해져있음

  : Consists of logic gates whose output at any time are determined from only the present combination of inputs. Perform an operation that can be specified logically by a set of Boolean functions and Truth table.

 

- Sequential Circuits: output = funtion(input 'and' present state) --> 입력이 있어도 출력이 확정되지 않음.

  : 자판기를 예시로 생각해보자. 150원짜리 커피를 살 때 100원을 집어넣어도 과거에 얼마를 넣었는지에 따라 커피가 나올  수도 있고 안나올 수도 있다. Employ storage elements in addition to logic gates. Their outputs are a function of the inputs and the state of the storage(memory) elements which is a function of the previous inputs. (The outputs of a sequential circuit depend not only on the present values of inputs, but also on the past inputs)

 

Combinational Circuits

- Outputs are determined from the present inputs.

- Consists of input variables, logic gates, and output variables.

 

Analysis vs Design

Anlysis: logic diagram -> boolean function and truth table

Design: boolean function and truth table -> logic diagram

 

Design of Combinational Circuits

- Start from the specification of the design objective and culminate in a logic circuit diagram or a set of Boolean functions.

- Procedure

  1) From the specifications of the circuit, determine the required inputs and outputs.

  2) Derive the truth table from inputs and outputs (= function spec).

  3) Obtain the simplified Boolean functions for each output by K-map.

  4) Draw the logic diagram and verify the correctness of the design.