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.