Computer Systems Nat 45 Computing Science Lesson 2

Computer Systems Nat 4/5 Computing Science Lesson 2: More on Binary

REVI SION 1. What is an integer? 2. Convert 1100 into a decimal number 3. Convert 23 into binary. 4. What are three advantages of binary

ANSW ERS 1. A whole number 2. 1100 = 204 3. 23 = 0001 0111 4. a) There are less rules of arithmetic. b) 0’s and 1’s are easier to represent. c) Any drop in voltage doesn’t effect data.

Lesson Aims By the end of this lesson you will be able to: Describe what a real number is. Describe what the mantissa is. Describe what the exponent is. Describe what Floating Point Representation is. Represent real numbers using Floating Point representation. State the storage terms used in computing.

Nat 4/5 What is a real number? Real numbers are ALL numbers both whole and fractional Real numbers can be 1¾ or 1. 75 or 1750 Real numbers can be very small 0. 00000001 or very large 1, 987, 897, 564, 859 Real numbers can be very accurate 1245. 235687412

Nat 4/5 How are real numbers represented in binary Real numbers are represented in binary using a system called floating point representation It is similar to floating point notation that is used in decimal to represent very small very large numbers For example 3*108 = 300. 000

Nat 4/5 Floating point representation In floating point notation, numbers can be divided into the base/mantissa/exponent a*10 b “a” is the mantissa (the number) 10 for the number system “b” the exponent (raises 10 to the power of) . 183506*102 = 18. 3506

Nat 4/5 Floating point representation 214 =. 214 * 1000 =. 214*103 mantissa The point moves three places base exponent

Nat 4/5 Floating point representation The mantissa is the actual digits of the number The exponent is the power (to which the base is raised) In binary the base is always 2 As the base is always 2 it can be ignored and all that has to be stored is, The mantissa (the number) and the exponent (the power to which the base is raised)

Nat 4/5 Floating point representation 214 = 11010110 in binary mantissa 11010110 =. 11010110 * exponent 1000 2 base The point moves eight places

Nat 4/5 Floating point representation We can ignore the base and leave out the multiplication sign and write it as: exponent 1101000 mantissa It exponent can also be written as 10110110 1000 mantissa

Nat 4/5 Storage terms used in computing A single unit in binary is a bit A bit can be 1 or 0 A binary number made up of eight bits is called a byte for example, 11101101 One Kilobyte is 1024 bytes, 1 Kb is one Kilobyte or 1024 bytes or 210 23 22 21 20

Nat 4/5 Storage terms used in computing 1 Kb = 1024 bytes One Megabyte (Mb) = 1024 Kilobytes (220 bytes) One Gigabyte (Gb) = 1024 Megabytes (230 bytes) One Terabyte (Tb) = 1024 Gigabytes (240 bytes) Sometimes the abbreviations are expressed in uppercase, KB, MB, GB and TB

Nat 4/5 Storage terms used in computing Kilobyte Megabyte

Nat 4/5 Megabyte Gigabyte

Nat 4/5 Storage terms used in computing Kilobyte Megabyte Gigabyte Terabyte Petabyte Exabyte Zettabyte Yottabyte A petabyte is the equivalent of 250 billion pages of text, enough to fill 20 million four-drawer filing cabinets.