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CSC 159- COMPUTER ORGANIZATIONCHAPTER 1B

Fundamental building blocksLogic GatesCountersRegisters PLABoolean AlgebraANDORNOTXORRegister transfer notation

LEARNING OUTCOMEComputers are built up from integrated circuits, each with its own purpose.

Integrated circuit are made up of transistors, resistors, capacitors and other electronic components that are combined into circuits.

In computer, these transistors switches are combined to form logic gates, which represent values in Boolean algebra.

Combinatorial logic the results of an operation depend only on the present input.

IntroductionLogic GatesDefinition: Gates is a block of hardware that produce a logic 1 or logic 0 output signal; if input logic requirements are satisfied3 WAYS TO REPRESENT LOGIC

ANDORNOTXORNANDNORBASIC GATES

COUNTERREGISTERPROGRAMMABLE LOGIC ARRAY (PLA) THE BASIC FORM OF PLA

As with a gate, a combinational circuit can be defined in 3 ways:

Truth Tableis used to describe the relationships of inputs and outputs in tabular formExample: There are 2 variables used, x and y. No. of combination = 2^2 = 4

Graphical Symbolsthe interconnected layout of gates is depicted

Boolean equations:Each output signal is expressed as a Boolean function of its input signalscan be used to describe the relationships of inputs and outputs in mathematical form.EXAMPLE : z = a + b + c

As with any algebra, Boolean algebra makes use of variables and operation In this case, the variables and operations are logical variables and operations

A AND B = A . BA OR B = A + BNOT A = AD = A + (B . C)D is equal to 1 if A is 1 or if both B = 0 and C = 1. Otherwise D is equal to 0This form expression, for self-evident reason is known as the sum of products (SOP) form.

Boolean Algebra

Boolean operators of 2 input variablesthe basic logical operations in a form known as a truth table, which lists the value of an operation for every possible combination of values of operands.

Boolean Operators

The table summarizes key identities of Boolean algebra.

These properties (Laws and Theorems) can be used tosimplify equations to their simplest form. Simplify F=XYZ+XYZ+XZ /

SIMPLY

Possible locations that may be involved in the transfers of information:

Memory locations; ex: LOC, PLACE,A,VAR2Processor registers; ex: R0,R5Registers in the I/O subsystem; ex: DATAIN, OUTSTATUSREGISTER TRANSFER NOTATIONthe contents of memory location LOC are transferred into processor register R1right-hand side of an RTN; denotes a valueleft-hand side; name of a location where the value is to be placed

EXAMPLER1[X]