2 Lesson Aims By the end of this lesson: You will be able to: Describe what an integer isRepresent positive integers in binary using up to 8 BitsState three advantages of the binary number systemRepresent negative numbers using binary (Nat 5)Represent real numbers using binary (Nat 5)
3 The Decimal & Binary Systems Nat 4/5The Decimal & Binary SystemsWe use the decimal(denary) or base 10 systemThis means we have 10 digits : 0-9Computers use the binary or base 2 systemThere are only two digits: 0 and 1Each figure is known as a bitBinary digitBecause of our ten fingers?Off and On
4 Nat 4/5Decimal NumbersLets look at how a decimal number is made up: 173Technically this is:HundredsTensUnits173102101100HundredsTensUnits173
5 Nat 4/5Binary NumbersBecause Binary is only made up of two digits (0 and 1) instead of 10 (as in Decimal), the column headings will be different.This is represented as:2423222120168421
6 Nat 4/5Binary NumbersLets look at how 173 is stored in binary:1286432168421The binary number is calculated by adding together the value of the columns with a 1.== 173
7 How to convert from Binary Nat 4/5How to convert from BinaryCreate your table with the values in the topInsert your binary value into the tableAdd the place values that have a binary 1 in them: = 10212864321684211
8 Advantages of the Binary system Nat 4/5Advantages of the Binary systemThere are less rules of arithmetic, this makes it easier to program.0’s and 1’s are easier to represent digitally in computer systems.Any drop in voltage does not affect the data.
9 Summary Binary only has two values– 0 & 1 Nat 4/5SummaryBinary only has two values– 0 & 1A single 0 or 1 is known as a bitBinary DigitThe place values in binary start on the right at 1 and double every time going to the left.Advantages of Binary:There are less rules of arithmetic.0’s and 1’s are easier to represent.Any drop in voltage doesn’t effect data.
10 What about negative numbers? Nat 5What about negative numbers?Integers include:--123, -89, 0, 45, , etcPositive and negative integers are represented using two’s complement
11 Two’s complement Write -7 :- +7 using 8 bits 0000 0111 Nat 5Two’s complementWrite -7 :-+7 using 8 bitsChange 1’s and 0’sAddSo -7 is
12 Nat 5Twos complement tasksQuestions 1 and 2 on Worksheet 1a
13 Real numbers Decimal Fractions:- 1/10 1/100 1/1000 …. As a fraction Nat 5Real numbersDecimal Fractions:-1/10 1/100 1/1000 …. As a fraction…. As a decimalBinary Fractions:-½ ¼ /8…. as a fraction…. as a decimal