Computer Systems

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Computer Systems - PowerPoint PPT Presentation

Computer Systems. Nat 4/5 Computing Science Lesson 1: Binary. Section Key Terms. KEY WORDS. Section Key Words. 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

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Computer Systems

Nat 4/5 Computing Science

Lesson 1:

Binary

Lesson Aims
• By the end of this lesson:
• You will be able to:
• Describe what an integeris
• Represent positive integers in binaryusing up to 8Bits
• State threeadvantages of the binary number system
Nat 4/5The Decimal & Binary Systems
• We use the decimal(denary) or base 10 system
• This means we have 10digits : 0-9
• Computers use the binary or base 2 system
• There are only twodigits: 0 and 1
• Each figure is known as a bit
• Binary digit

Because of our ten fingers?

Off and On

Nat 4/5Decimal Numbers
• Lets look at how a decimal number is made up: 173
• Technically this is:
Nat 4/5Binary Numbers
• Lets look at how the same number is stored in binary: 1010 1101
• This number is constructed as shown above.
• These values come from:
Nat 4/5How to convert into Binary
• Let’s look at the same example:
• 173/2 = 86 r 1
• 86/2 = 43 r 0
• 43/2 = 21 r 1
• 21/2 = 10 r 1
• 10/2 = 5 r 0
• 5/2 = 2 r 1
• 2/2 = 1 r 0
• 1/2 = 0 r 1
• Binary Number = 1010 1101

Our binary number is:

1010 1101

Read the binary number from bottom up

.

This is our binary number

Nat 4/5How to convert into Binary
• Using the number 173 earlier. The aim is to subtract the values from the number until we are left with 0.
• Can we subtract 128 from 173?
• Yes – So we add a 1 to our number
• Can we subtract 64 from 45?
• No so we add a 0
• Can we subtract 32 from 45?
• Yes so we add a 1
• Can we subtract 16 from 13?
• No so we add a 0
• Can we subtract 8 from 13?
• Yes so we add a 1
• Can we subtract 4 from 5?
• Yes so we add a 1
• Can we subtract 2 from 1?
• No so we add a 0
• Can we subtract 1 from 1?
• Yes so we add a 1

Read the binary number from top down

Our binary number is:

1010 1101

Nat 4/5How 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: 64+32+4+2 = 102
Nat 4/5Summary
• 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.