7
Arithmetic Circuits
Beginning with this chapter, and in the two chapters following, we will take a comprehensive look
at various building blocks used to design more complex combinational circuits. A combinational
logic circuit is one where the output or outputs depend upon the present state of combination of
the logic inputs. The logic gates discussed in Chapter 4 constitute the most fundamental building
block of a combinational circuit. More complex combinational circuits such as adders and subtractors,
multiplexers and demultiplexers, magnitude comparators, etc., can be implemented using a combination
of logic gates. However, the aforesaid combinational logic functions and many more, including more
complex ones, are available in monolithic IC form. A still more complex combinational circuit may
be implemented using a combination of these functions available in IC form. In this chapter, we
will cover devices used to perform arithmetic and other related operations. These include adders,
subtractors, magnitude comparators and look-ahead carry generators. Particular emphasis is placed
upon the functioning and design of these combinational circuits. The text has been adequately
illustrated with the help of a large number of solved problems, the majority of which are design
oriented.
7.1 Combinational Circuits
A combinational circuit is one where the output at any time depends only on the present combination
of inputs at that point of time with total disregard to the past state of the inputs. The logic gate is the
most basic building block of combinational logic. The logical function performed by a combinational
circuit is fully defined by a set of Boolean expressions. The other category of logic circuits, called
sequential logic circuits, comprises both logic gates and memory elements such as flip-flops. Owing to
the presence of memory elements, the output in a sequential circuit depends upon not only the present
but also the past state of inputs. Basic building blocks of sequential logic circuits are described in
detail in Chapters 10 and 11.
Figure 7.1 shows the block schematic representation of a generalized combinational circuit having
n input variables and m output variables or simply outputs. Since the number of input variables is
Digital Electronics: Principles, Devices and Applications Anil K. Maini
© 2007 John Wiley & Sons, Ltd. ISBN: 978-0-470-03214-5
Arithmetic Circuits
Beginning with this chapter, and in the two chapters following, we will take a comprehensive look
at various building blocks used to design more complex combinational circuits. A combinational
logic circuit is one where the output or outputs depend upon the present state of combination of
the logic inputs. The logic gates discussed in Chapter 4 constitute the most fundamental building
block of a combinational circuit. More complex combinational circuits such as adders and subtractors,
multiplexers and demultiplexers, magnitude comparators, etc., can be implemented using a combination
of logic gates. However, the aforesaid combinational logic functions and many more, including more
complex ones, are available in monolithic IC form. A still more complex combinational circuit may
be implemented using a combination of these functions available in IC form. In this chapter, we
will cover devices used to perform arithmetic and other related operations. These include adders,
subtractors, magnitude comparators and look-ahead carry generators. Particular emphasis is placed
upon the functioning and design of these combinational circuits. The text has been adequately
illustrated with the help of a large number of solved problems, the majority of which are design
oriented.
7.1 Combinational Circuits
A combinational circuit is one where the output at any time depends only on the present combination
of inputs at that point of time with total disregard to the past state of the inputs. The logic gate is the
most basic building block of combinational logic. The logical function performed by a combinational
circuit is fully defined by a set of Boolean expressions. The other category of logic circuits, called
sequential logic circuits, comprises both logic gates and memory elements such as flip-flops. Owing to
the presence of memory elements, the output in a sequential circuit depends upon not only the present
but also the past state of inputs. Basic building blocks of sequential logic circuits are described in
detail in Chapters 10 and 11.
Figure 7.1 shows the block schematic representation of a generalized combinational circuit having
n input variables and m output variables or simply outputs. Since the number of input variables is
Digital Electronics: Principles, Devices and Applications Anil K. Maini
© 2007 John Wiley & Sons, Ltd. ISBN: 978-0-470-03214-5