digital components and combinational circuits sachin kharady
TRANSCRIPT
Digital Components and Combinational Circuits
Sachin Kharady
SECTION 3.4Digital Components
• 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
SECTION 3.5Combinational Circuits
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.