Digital Components and Combinational Circuits Sachin Kharady

SECTION 3.4 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 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 3.5 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.

Decoder A decoder decodes binary info from a set of n inputs to a maximum of 2 n 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.