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**Nat 4/5 Computing Science Lesson 1: Binary**

Computer Systems Nat 4/5 Computing Science Lesson 1: Binary

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**Lesson Aims By the end of this lesson: You will be able to:**

Describe what an integer is Represent positive integers in binary using up to 8 Bits State three advantages of the binary number system Represent negative numbers using binary (Nat 5) Represent real numbers using binary (Nat 5)

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**The Decimal & Binary Systems**

Nat 4/5 The Decimal & Binary Systems We use the decimal(denary) or base 10 system This means we have 10 digits : 0-9 Computers use the binary or base 2 system There are only two digits: 0 and 1 Each figure is known as a bit Binary digit Because of our ten fingers? Off and On

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Nat 4/5 Decimal Numbers Lets look at how a decimal number is made up: 173 Technically this is: Hundreds Tens Units 1 7 3 102 101 100 Hundreds Tens Units 1 7 3

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Nat 4/5 Binary Numbers Because 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: 24 23 22 21 20 16 8 4 2 1

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Nat 4/5 Binary Numbers Lets look at how 173 is stored in binary: 128 64 32 16 8 4 2 1 The binary number is calculated by adding together the value of the columns with a 1. = = 173

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**How to convert from Binary**

Nat 4/5 How to convert from Binary Create your table with the values in the top Insert your binary value into the table Add the place values that have a binary 1 in them: = 102 128 64 32 16 8 4 2 1 1

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**Advantages of the Binary system**

Nat 4/5 Advantages of the Binary system There 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.

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**Summary Binary only has two values– 0 & 1**

Nat 4/5 Summary Binary only has two values– 0 & 1 A single 0 or 1 is known as a bit Binary Digit The 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.

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**What about negative numbers?**

Nat 5 What about negative numbers? Integers include:- -123, -89, 0, 45, , etc Positive and negative integers are represented using two’s complement

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**Two’s complement Write -7 :- +7 using 8 bits 0000 0111**

Nat 5 Two’s complement Write -7 :- +7 using 8 bits Change 1’s and 0’s Add So -7 is

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Nat 5 Twos complement tasks Questions 1 and 2 on Worksheet 1a

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**Real numbers Decimal Fractions:- 1/10 1/100 1/1000 …. As a fraction**

Nat 5 Real numbers Decimal Fractions:- 1/10 1/100 1/1000 …. As a fraction …. As a decimal Binary Fractions:- ½ ¼ /8 …. as a fraction …. as a decimal

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Real numbers task Question 3 on Worksheet 1a

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**Floating point representation**

From Maths we know that:- = x 102 Mantissa x Base Exponent In binary :- = = x 2 101 5 in decimal is 101 in binary

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**Floating point representation**

Nat 5 Floating point representation The computer stores the mantissa & exponent of a real number x 2 101 Mantissa = Exponent = 101

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Nat 5 Floating point task Question 4 Worksheet 1a

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