Computer Systems

1 / 18

# Computer Systems - PowerPoint PPT Presentation

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 integer is Represent positive integers in binary using up to 8 Bits State three advantages of the binary number system

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Computer Systems' - chin

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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
• Represent negative numbers using binary (Nat 5)
• Represent real numbers using binary (Nat 5)
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
• 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:
Nat 4/5Binary Numbers
• Lets look at how 173 is stored in binary: 1010 1101
• The binary number is calculated by adding together the value of the columns with a 1.
• = 128 + 32 + 8 + 4 + 1
• = 173
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.

• There are less rules of arithmetic.
• 0’s and 1’s are easier to represent.
• Any drop in voltage doesn’t effect data.
• Integers include:-
• -123, -89, 0, 45, 109876, etc
• Positive and negative integers are represented using two’s complement
Nat 5Two’s complement
• Write -7 :-
• +7 using 8 bits 0000 0111
• Change 1’s and 0’s 1111 1000
• So -7 is 1111 1001
• Questions 1 and 2 on Worksheet 1a
Nat 5Real numbers
• Decimal Fractions:-
• 1/10 1/100 1/1000 …. As a fraction
• 0.1 0.01 0.001 …. As a decimal
• Binary Fractions:-
• ½ ¼ 1/8
• 0.5 0.25 0.125 …. as a fraction
• 0.1 0.01 0.001 …. as a decimal
• Question 3 on Worksheet 1a
Floating point representation
• From Maths we know that:-
• 20.125 = .20125 x 102
• Mantissa x Base Exponent
• In binary :-
• 20.125 = 10100.001 = .10100001 x 2 101

5 in decimal is 101 in binary

Nat 5Floating point representation
• The computer stores the mantissa & exponent of a real number
• .10100001 x 2 101
• Mantissa = 10100001
• Exponent = 101