This document discusses data storage and representation in computers. It covers different types of data like discrete and continuous data. It also discusses number systems like the decimal and binary systems. The decimal system uses base 10 with digits 0-9, while the binary system uses base 2 with digits 0 and 1. The document explains how to perform binary addition and subtraction. It also discusses representing signed numbers in binary using methods like sign-magnitude, one's complement, and two's complement representations. Finally, it provides an example of a 4-bit binary representation of decimal numbers between -7 and +7.

1. Data Storage & RepresentationHow data is stored in the Computer

2. DataAs you may recall data is raw facts that cannot take the form of letters, numbers, text , sound and images.There are two types of dataDiscrete DataDATAContinuous Data

6. DECIMAL NUMBER SYSTEMBefore we explain the concept of the binary system, let us review the number system we are familiar with. Our decimal number system consists of ten digits: 0,1,2,3,4,5,6,7,8,9 and for this reason it is referred to as the base 10 number system or denary.The base of any number may be indicated as a subscript on the extreme right of the number e.g.45510

7. Types of numbers in the denary systemNatural numbers or whole numbers such as -1,2,3,10,108 etc.Integers are numbers that have no fractional parts and are either positive or negative. -19,88,-9etc.Real numbers are numbers with a decimal point or include a fractional part. 10.8, -8.9 etcThe magnitude of a number refers to how large a number is. It does not depend on the sign of a number. E.gthe magnitude of -10 and 10 is 10.

8. Binary AdditionTo Lean 5 binary sumsOctal number systemHexadecimal number systemBinary subtraction

9. Representing Signed NumbersSigned numbers are both positive and negative integers. (an integer is a whole number with no fractional part)Ways of representing signed numbers areSign and magnitudeOne’s complementTwo’s complementBinary coded decimal

10. Sign & Magnitude representationThe leftmost bit is used to represent the sign (positive or negative) and the remaining bits represent the magnitude.A ‘0’ sign bit indicates that the number is positive.A ‘1’ sign bit indicates that the number is negative. 00101101Sign bitmagnitude

11. 4 bit binary representation of the decimal systemThe range of numbers that can be represented using four bits is -7 to +7