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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

Computer Systems

Nat 4/5 Computing Science

Lesson 1:

Binary

lesson aims
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
the decimal binary systems
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

decimal numbers
Nat 4/5Decimal Numbers
  • Lets look at how a decimal number is made up: 173
  • Technically this is:
binary numbers
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:
how to convert into binary
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

how to convert into binary1
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

how to convert from binary
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
summary
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.

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.