Transcript Digital Components and Combinational Circuits

Digital Components and
Combinational Circuits
Sachin Kharady
Digital Components
SECTION 3.4
• All digital components inside a computer are
essentially built with collections of gates.
• All gates use Boolean algebra to accomplish
tasks.
• Two categories of logic – combinational logic,
and sequential logic
Relationship to Boolean algebra
• Logic diagrams can be built to represent
functions as well as physical circuits
• The complexity of a Boolean function reflects
the complexity of the circuit
Integrated circuits
• Typically, gates are sold as units called
integrated circuits.
• A chip is a small electronic device consisting of
various gates.
• The chips already consist various electrical
components such as transistors, resistors and
capacitors to implement gates
• The necessary
connections are welded
from the chip to the
external pins to form an
IC.
• First ICs contained up to
100 components per
chip, but now it has
grown to more than 1
million
Combinational Circuits
SECTION 3.5
Basic concepts
• Combinational logic is used to build
circuits that contain basic Boolean
operators, inputs and outputs.
• The output is a function of the inputs.
Typical Combinational Circuits
• Half-adder – specifies a
circuit with two inputs
to add two binary digits,
and two outputs – one
for sum, and one for
carry.
– The sum is an XOR gate
and the carry is an AND
gate
Full Adder
• Full-Adder – consists of two half adders and an OR
gate
• To add a 16-bit word, this circuit is replicated 16
times to create the ripple carry adder.
Decoder
• A decoder decodes binary info
from a set of n inputs to a
maximum of 2n inputs.
• It uses inputs and their
respective values to select one
specific output line. – it means
that one output is set to 1 and
all others are set to 0
• 3-to-8 decoder – 3 inputs and
8 outputs.
• Computer memory is written
in binary numbers and and to
determine the address of a
stored block, a decoder is
used.
Multiplexer
• Selects binary info from on of many input lines
and directs it to a single output line.
• Selection is base on a couple of control lines
Parity
• Parity Generator and parity checker circuits
– Parity generator – creates the necessary partiy bit
to add to a word
– Parity checker – checks to make sure proper parity
(odd or even) is present in the word, detecting an
error if the parity bit is incorrect.
Arithmetic Logic Unit
• Consists of these
combinational circuits
• Carries out at least four
basic operations, AND,
OR, NOT and addition.