Digital Components and Combinational Circuits

Digital 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 of 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. Weld = لحام

Combinational 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. ripple = تموّج

Decoder A decoder decodes binary info from a set of n inputs to a maximum of 2n input. 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 to determine the address of a stored block, a decoder is used. For example, only xy is going to be 1 and all of other output are going to be 0 x’y, xy’ and x’y’

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 parity 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.

Odd Parity, the number of ones should odd

Arithmetic Logic Unit Consists of these combinational circuits Carries out at least four basic operations, AND, OR, NOT and addition.

This Summary is an Online Content from this Book: Morris Mano, DIGITAL DESIGN, 4th Edition, Prentice Hall, 2007 It is edited for Logic Analysis and Design Course 6803213-3 by: T.Mariah Sami Khayat Teacher Assistant @ Adam University College For Contacting: mskhayat@uqu.edu.sa Kingdom of Saudi Arabia Ministry of Education Umm AlQura University Adam University College Computer Science Department المملكة العربية السعودية وزارة التعليم جامعة أم القرى الكلية الجامعية أضم قسم الحاسب الآلي