Starter Using the fingers on only one hand, what is the highest number you can count to? Rules: You must start at 1 You must count sequentially (i.e. 1, 2, 3…) For each number you cannot use a finger more than once

Learning Intention I will learn how computers store whole numbers (Integers)

The Decimal System We use the decimal or base 10 system in normal life: This means we have 10 digits: 0-9

The Binary System Computers use the binary or base 2 system: There are two digits: 0 and 1 Each figure is known as a bit (binary digit)

Decimal Numbers Look at how a decimal number is made up: e.g. 273 273 = (2 x 100) + (7 x 10) + (3 x 1) Hundreds 103 = 100 Tens 102 = 10 Units 101 = 1 2 7 3

Binary Numbers The column headings for 8-bit binary numbers are: 128 64 32 16 8 4 2 1

Converting Binary to Decimal Lets look at how 23 is stored in binary: = (1 x 16) + (1 x 4) + (1 x 2) + (1 x 1) = 16 + 4 + 2 + 1 = 23 128 64 32 16 8 4 2 1

Steps to convert from Binary to Decimal Write the binary column headings Write the binary number below the headings Add up the column headings that have a 1: 64 + 32 + 8 + 2 = 106 128 64 32 16 8 4 2 1 128 64 32 16 8 4 2 1

Try these: Convert from Binary to Decimal: 00001110 =8+4+2=14 00101011 01111001 =8+4+2=14 =32+8+2+1=43 =64+32+16+8+1=121

Complete Task 2 questions 1 to 5 Remember to use the column headings to help you: 128 64 32 16 8 4 2 1

Success Criteria I know how computers store numbers and can convert from binary to decimal.

There are only 10 kinds of people in the world There are only 10 kinds of people in the world. Those who understand binary and those who don’t.

Learning Intention I will learn how to convert from decimal into binary.

Converting Decimal to Binary Let’s look at how to write the decimal value 145 in binary: = 128 + 16 + 1 = 145 128 64 32 16 8 4 2 1

Steps to convert from Decimal to Binary E.g. for the Decimal number 89 Write the column headings 128 64 32 16 8 4 2 1

Try these: Convert from Decimal to Binary: 1 1 1 15 1 73 114 212 128 64 32 16 8 4 2 1 1 1 1 1

Complete Task 2 questions 6 and 7 Remember to use the column headings to help you: 128 64 32 16 8 4 2 1

Success Criteria I can convert from decimal into binary.

Learning Intention I will learn how computers store real numbers

These are stored using floating point representation. Storing real numbers Computers need to be able to store real numbers (e.g. 3678.2521), not just whole numbers. These are stored using floating point representation.

In maths you would store a floating point number such as 20 In maths you would store a floating point number such as 20.25 as follows in standard form: 0.2025 x 102 m x 10e mantissa exponent

Storing real numbers (cont) Computers store floating point numbers by storing the binary values for the mantissa and exponent

Success Criteria I can describe how computer store real numbers.