Digital Logic 2070

Full subtractor contains 3 inputs and 2 outputs (Difference and Borrow) as shown-

The truth table for full subtractor:

From the above truth table,

For the different functions in the truth table, the minterms can be written as 1,2,4,7, and similarly, for the borrow, the minterms can be written as 1,2,3,7. 

Since there are three inputs and a total of eight minterms. So we need 3-to-8 line decoder. The decoder generates the eight minterms for A, B & B_in.

Fig: Full subtractor with 3-to-8 Decoder and NOR gates

Solⁿ:

Input variables: A & B,       Output variables: sumand carry

Logic diagram of half adder using NAND gates only:

Combinational circuit is a circuit which consist of logic gates whose outputs at any instant of time are determined directly from the present combination of inputs without regard to previous input. The combinational circuit do not use any memory.

• There will be combination of input variable for inputs.

• A combinational circuit can have number of inputs and number of outputs.

• For e.g. adders, subtractors, decoders, encoders etc.

  
  

Fig: Block diagram of combinational circuit

Combinational logic circuit design procedure:

1. The problem is stated.

2. The number of available input variables and required output variables is determined.

3. The input and output variables are assigned letter symbols.

4. The truth table that defines the required relationships between inputs and outputs is derived.

5. The simplified Boolean function for each output is obtained.

6. The logic diagram is drawn.

Adders

Adders are the combinational circuits which is used to add two or more than two bits at a time.

Types of adders:

• Half Adder

• Full Adder

1. Half Adder:

A combinational circuit that performs the addition of bits is called half adder. This circuit needs two binary inputs and two binary outputs. The input variables designate the augend and addend bits; the output variables produce the sum and carry.

Fig: Block diagram