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Computer Systems

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

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

  2. 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)

  3. Nat 4/5 The 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

  4. Nat 4/5 Decimal Numbers • Lets look at how a decimal number is made up: 173 • Technically this is:

  5. 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:

  6. Nat 4/5 Binary 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

  7. 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: 64+32+4+2 = 102

  8. Nat 4/5 Advantages of the Binary system

  9. 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.

  10. Nat 5 What about negative numbers? • Integers include:- • -123, -89, 0, 45, 109876, etc • Positive and negative integers are represented using two’s complement

  11. Nat 5 Two’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

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

  13. Nat 5 Real 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

  14. Real numbers task • Question 3 on Worksheet 1a

  15. 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

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

  17. Nat 5 Floating point task • Question 4 Worksheet 1a

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