Memory & Storage: Lesson 5 Storing Numbers, Slides of Computer science

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Memory & Storage: Lesson 5

Starter

1. What is 7 in binary?
2. What is 1001 in denary?

Memory & Storage: Lesson 5

Storing Numbers

Learning Outcomes:

1. Convert positive denary whole numbers (0-255) into 2 - digit hexadecimal numbers and vice versa
2. Convert between binary, denary and hexadecimal equivalents of the same number
3. Add two 8 - bit binary integers and explain overflow errors which may occur
4. Understand the use of binary shifts

Memory & Storage: Lesson 5

Storing Numbers

Memory & Storage: Lesson 5

Hex to denary conversion

• You will only need to translate one- or two-digit hexadecimal numbers
• Multiply the left-hand digit by 16, then add the units
• What is hex 27 in denary? 16s Units 2 A 2x16 + 10 = 42 in denary

Memory & Storage: Lesson 5

Denary to hex conversion

1. Divide the denary number by 16 to get the number of 16s (the left-hand hex digit)
2. The remainder gives you the units Denary 18 becomes: 18 / 16 = 1 remained 2 so the hex value for 18 is 1 2 ( Spoken, ‘One Two’, not ‘Twelve’ )

• What is denary 27 in hex?
• What is denary 44 in hex?

Memory & Storage: Lesson 5

Binary to hex conversion

1. Take a binary word of 8 bits 1 1 1 0 0 1 0 1
2. Divide into two nibbles of 4 bits 1 1 1 0 0 1 0 1
3. Convert each nibble into its hex value and re-join 1 1 1 0 = 14 = E in Hex + 0 1 0 1 = 5 in Hex So 1 1 1 0 0 1 0 1 = E5 in Hex

Memory & Storage: Lesson 5

Hex to binary conversion

What is 3B in hex? Split the two hex characters 3 = 0011 in binary and B = 1011 So 3B = 0011 1011 in binary

• What is hex 21 in binary?
• What is hex A5 in binary?

Memory & Storage: Lesson 5

Why use hex?

• There are advantages for programmers and Computer Scientists in using hex rather than binary - It is much simpler to remember a hex value than a binary value - It is quicker to write or type since a hex digit only takes up one digit rather than 4 bits - People are less likely to make an error with fewer digits - It is easy to convert between hex and binary

Memory & Storage: Lesson 5

Task 1:

Hexadecimal

Complete Task 1 on the worksheet Navigation: 🠀 Student G-Suite 🠀 Computer Studies 🠀 GCSE Computer Science 🠀 Unit 1: Computer Systems 🠀 1.2: Memory & Storage 🠀 Lesson 5: Storing Numbers 🠀 Worksheet 1

Memory & Storage: Lesson 5

Binary addition

Use binary to add two numbers together

Memory & Storage: Lesson 5

Simple denary addition

Work right to left :

1. Add the Units
2. If Over 9, Carry Tens
3. Add Tens 1 4 1 7 3 1

= 1

Memory & Storage: Lesson 5

Adding binary values

0 1 0 1 1 1 1 1 1 0 0

= 1 1 1 1 1 Carry

Memory & Storage: Lesson 5

Adding numbers

• Computers work with a fixed number of bits at a time
  • This can cause problems
  • What problem will arise when adding the following bytes and storing the result in one byte? 1 1 1 1 0 0 0 0

• 1 0 0 1 1 1 1 1

Memory & Storage: Lesson 5

Task 2:

Binary Sums

Complete Task 2 (Q1-9) on the worksheet Navigation: 🠀 Student G-Suite 🠀 Computer Studies 🠀 GCSE Computer Science 🠀 Unit 1: Computer Systems 🠀 1.2: Memory & Storage 🠀 Lesson 5: Storing Numbers 🠀 Worksheet 1

Memory & Storage: Lesson 5

Logical binary shift operations

• A binary shift left of one bit moves all the bits one place to the left
  • The vacant bit spaces are filled with zeros
• Looking at the table above, what effect does a shift left of one place have on the binary value? What effect would a shift right of two places have? 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0