Question 2 - Figure it out - Page 69 - Chapter 3 Class 8 - A Story of Numbers (Ganita Prakash)

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Question 2 Create your own number system of base 4, and represent numbers from 1 to 16.To create a Base-4 system, our "Landmark Numbers" must be powers of 4. 4^0=𝟏 4^1=𝟒 4^2=4×4=𝟏𝟔 Let's invent symbols for these landmarks: Let a Dot (•) represent 1. Let a Plus (+) represent 4. Let a Star ( ⋆ ) represent 16. Representation of Numbers 1 to 16: Decimal Base-4 Code Visual Representation Calculation 1 14 ◯ 2 24 ◯ 3 34 ◯ ◯ 4 104 5 114 6 +00 7 134 8 204 9 214 10 224 11 234 12 13 14 324 15 16 In this system, you can never have 4 of the same symbol. As soon as you get 4 dots, they turn into 1 Plus. As soon as you get 4 Pluses, they turn into 1 Star. Let’s look at more detailed calculation of Numbers 6, & 15in our number system Representing 6 in Number System Base-4 Number System Representing numbers using Landmark Powers of 4 ◯ Dot Plus Star = 16 Choose a Number (Decimal) 6 1 Visual Breakdown 4S PLACE (Groups of 4) 1S PLACE (Groups of 1) ◯ Base-4 Representation 124 8 12 16 O Mathematical Proof:Representing 15 in Number System Base-4 Number System Representing numbers using Landmark Powers of 4 ◯ Dot = 1 Plus = 4 Star = 16 Choose a Number (Decimal) 15 Base-4 Representation 334 1 4 8 12 16 /isual Breakdown 4S PLACE (Groups of 4) 1S PLACE 3 (Groups of 1) ◯ ◯ ◯ Mathematical Proof: