*(ii) Design of full-adders*

A full adder is a combination logic circuit that uses three inputs (A, B and Cin) and two outputs (Sum S and Carry C). **Table 2** shows the truth table the various combinations of inputs and its corresponding outputs. The output Sum S and Carry C is obtained and the k-map is used to get the logical equation.


**Table 1.** *Truth Table – Half Adder.*

*3.2.2 Subtractor circuits*

*DOI: http://dx.doi.org/10.5772/intechopen.97611*

*Digital System Design*

*(i) Design of half-subtractor*

*(ii) Design of Full-subtractor*

**Table 3.**

**Figure 4.**

**161**

*Truth Table – Half Subtractor.*

*Logic Diagram – Half Subtractor.*

B, the outputs are Difference and Borrow

A combinational circuit that performs the difference of two bits is called *halfsubtractor*. When the first input (minuend) is 0 and the second input(subtrahend) is 1 then there exists a output variable as *Borrow.* The combinational circuit that

A half subtractor is a combination logic circuit that uses two inputs (A and B) and two outputs (Difference D and Borrow B). **Table 3** shows the truth table the various combinations of inputs and its corresponding outputs. The output Difference D and Borrow B is obtained and the k-map is used to get the logical equation. **Figure 4** shows the design and implementation of half subtractor circuit in LabVIEW environment, where the front panel that two inputs Input A and Input

A full subtractor is a combination logic circuit that uses three inputs (A, B and Bin) and two outputs (Difference D and Borrow B). **Table 4** shows the truth table the various combinations of inputs and its corresponding outputs. The output difference D and Borrow B is obtained and the k-map is used to get the logical equation

**A B Difference D Borrow B** 000 0 01 1 1 101 0 110 0

*Input Variables Output Variables*

*Difference* ¼ *A*⨁*B* (5) *Borrow* ¼ *AB* (6)

*Difference D* ¼ *A*⨁*B*⨁*Bin* (7) *Borrow B* ¼ *AB* þ *A*⨁*B* (8)

determines the difference of three bits is called a *full-subtractor*.

**Figure 2.** *Logic Diagram – Half Adder.*


**Figure 3.** *Logic Diagram – Full Adder.*

$$\text{Carry C} = AB + BC\_{in} + C\_{in}A \tag{4}$$

**Figure 3** shows the design and implementation of full adder circuit in LabVIEW environment, where the front panel that two inputs Input A, Input B, and Input Cin, the outputs are Sum and Carry. The block diagram in LabVIEW environment shows the logic gate implementation for the above obtained expression.
