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###Getting Down to Business with Binary This is a group lab, so make sure you are working in a group of 2-4 students

To start this lab, let's count to ten. Ok, fine, any 3 year old could count to ten. But can you count to ten in binary? How about in hexadecimal? Not so easy...yet!

The number system we use is called the decimal number system. We say it is base 10 because it uses 10 digits from 0 to 9. But what happens when we count past 9? We don't have a single symbol for 10, so you have to add 1 in a new column and then start over again at 0 in the ones place.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9...now start over by adding a new column (the tens place) worth ten times the first column (the ones place) 10, 11, 12...

Other systems use different bases. Binary, for example, is base 2. Because of this, we only have two digits we count with: 0 and 1. Let's see how that works. You count 0, 1, then you have to start over at zero and add a column! The next column is worth twice the value of the first column. Since binary is a base 2 system, each digit represents a power of 2, with the rightmost digit representing 2⁰ (0), the next representing 2¹ (2), then 2² (4), 2³ (8) and so on.

Decimal | Binary | Explanation

• | ------ | ----------- 0 | 0 | Start at zero 1 | 1 | Then 1 2 | 10 | Start back at zero, add 1 to the left 3 | 11 | 4 | 100 | Start all numbers back at zero again, add one to the left again 5 | 101 | One in the fours place, one in the ones place 6 | 110 | One in the fours place, one in the twos place 7 | 111 | One in the fours place, one in the twos place, one in the ones place 8 | 1000 | One in the eights place

• Create a method called decimal_to_binary that converts a decimal number to its binary equivalent. Your method should take in a decimal as an argument and output it as binary.

• Create a method called binary_to_decimal that converts a binary number to its decimal equivalent. Your program should take in a binary number and output it as a decimal.

Write your code in the binary.rb file. Run learn to see if your code passes the tests written for it. You should be able to successfully convert the following decimal numbers to binary and binary numbers to decimal:

Decimal | Binary

• | ------ 1 | 1 2 | 10 13 | 1101 34 | 100010 100 | 1100100 526 | 1000001110

Google the hexadecimal number system. It works just like binary or decimal, but has a base of 16. Once you've figured out how hexadecimals work, create a program that converts a decimal number to its hexadecimal equivalent, and vice versa (as above). Write your code in the hexadecimal.rb file.

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