Design of Combinational Circuits




Design of Combinational Circuits

Desighn of combinational circuits starts from the verbal outline of the problem and ends in a logic circuit diagram the procedure involves following steps:-

  • State the given problem completely and exactly.

  • Interpet the problem to determine available input variable and required output variables.

  • Assign a letter symbol to each input variable and each output variable.

  • Design a truth table that defines the required relations between inputs and outputs.

  • Obtain simplified Boolean expression for each output.

  • Draw a logic circuits diagram to implement the Boolean expressions.

The design-procedure is illustrated below with the design of adder circuits because addition is the most basic arithmetic operation for any computer system.

The following four rules summarize addition in binary system -

0+0=0
	0+1=1
	1+0=1
	1+1=0

The first three operations produce a single-digit sum, but when both augend and addend bits are equal to 1, the sum consists of two digits. The higher significant bit of this result is called a carry. When the augend and added numbers contain more than one digit, the carry obtained from the addition of two bits at any stage is added to the next pair of significant bits. A combinational circuit that performs the addition of two bits is called a half- adder. One that perfoms the addition of three bits (two-significant bits and previous carry) is called a full-adder. The name of the former comes from the fact that we can implement a full-adder by using two half=adders.