Converting from Base-n to Base-10

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Presentation transcript:

Converting from Base-n to Base-10 ID1050– Quantitative & Qualitative Reasoning Here is a note inserted by me.

Steps for Converting from Base-n to Base-10 The steps for converting from a different base to our familiar base-10 (decimal) system are similar to how we express numbers in base-10 Each column has a different value which depends on the base Each column has a digit in it that is multiplied by the column’s value The sum of all of these multiplication results is the value of the number The difference is that the columns have values other than ‘tens’, ‘hundreds’, ‘thousands’, etc. Let’s look at some examples: Comparison to base-10.

Base-8 Positional Notation Chart 83 = 512 82 = 64 81 = 8 80 = 1 8-1 = 1/8 8-2 = 1/64 ____________ Answer: 16 Convert 20base-8 to base-10 Only Base-8 digits 0,1,2,3,4,5,6,7

Base-8 Positional Notation Chart 83 = 512 82 = 64 81 = 8 80 = 1 8-1 = 1/8 8-2 = 1/64 ____________ Answer: 5/16 = 0.3125 Convert 0.24base-8 to base-10 Only Base-8 digits 0,1,2,3,4,5,6,7

Base-8 Positional Notation Chart 83 = 512 82 = 64 81 = 8 80 = 1 8-1 = 1/8 8-2 = 1/64 ____________ Answer: 450.125 Convert 702.1base-8 to base-10 Only Base-8 digits 0,1,2,3,4,5,6,7

Base-3 Positional Notation Chart 33 = 27 32 = 9 31 = 3 30 = 1 3-1 = 1/3 3-2 = 1/9 ____________ Answer: 15 Convert 120base-3 to base-10 Only Base-3 digits 0,1,2

Base-3 Positional Notation Chart 33 = 27 32 = 9 31 = 3 30 = 1 3-1 = 1/3 3-2 = 1/9 ____________ Answer: 2.33333333 Convert 2.1base-3 to base-10 Only Base-3 digits 0,1,2

Base-2 (binary) Positional Notation Chart 23 = 8 22 = 4 21 = 2 20 = 1 2-1 = 1/2 2-2 = 1/4 ____________ Answer: 10 Convert 1010base-2 to base-10 Only Base-2 digits 0,1

Base-2 (binary) Positional Notation Chart 23 = 8 22 = 4 21 = 2 20 = 1 2-1 = 1/2 2-2 = 1/4 ____________ Answer: ¾ = 0.75 Convert 0.11base-2 to base-10 Only Base-2 digits 0,1

Base-2 (binary) Positional Notation Chart 23 = 8 22 = 4 21 = 2 20 = 1 2-1 = 1/2 2-2 = 1/4 ____________ Answer: 2 ¼ = 2.25 Convert 10.01base-2 to base-10 Only Base-2 digits 0,1

Conclusion Converting from a different base into base 10 involves creating a base-n table The columns in base-n have different values than our familiar base-10 columns Multiply each base-n digits by its column’s value and add them all up to get the answer in base-10