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

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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
  • Represent negative numbers using binary (Nat 5)
  • Represent real numbers using binary (Nat 5)
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
  • 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:
binary numbers1
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
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.
what about negative numbers
Nat 5What about negative numbers?
  • Integers include:-
  • -123, -89, 0, 45, 109876, etc
  • Positive and negative integers are represented using two’s complement
two s complement
Nat 5Two’s complement
  • Write -7 :-
  • +7 using 8 bits 0000 0111
  • Change 1’s and 0’s 1111 1000
  • Add 1 + 1
  • So -7 is 1111 1001
twos complement tasks
Nat 5Twos complement tasks
  • Questions 1 and 2 on Worksheet 1a
real numbers
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
real numbers task
Real numbers task
  • Question 3 on Worksheet 1a
floating point representation
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

floating point representation1
Nat 5Floating point representation
  • The computer stores the mantissa & exponent of a real number
  • .10100001 x 2 101
  • Mantissa = 10100001
  • Exponent = 101
floating point task
Nat 5Floating point task
  • Question 4 Worksheet 1a