Project 95: Decimal to Binary

Binary is as easy as "1, 10, 111"

Difficulty Level: High

Converting from Decimal to Binary

Example 1: 50 base 10 to base 2

Think about the powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256,…

The highest power of 2 that is less than or equal to 50 is 2^5 = 32

To decompose 50 into sum of powers of 2, we need a 32 (2^5).  This would leave 18 (50 -32).

The highest power of 2 that is less than or equal to 18 is 2^4 = 16.  This would leave 2 (50 – 32 – 16).

The highest power of 2 that is less than or equal to 2 is 2^1 = 2.  This would leave 0.

50 = 1*2^5 + 1*2^4 + 0*2^3 + 0*2^2 + 1*2^1 + 0*2^0.

50 base 10 can be written as follows in binary: 110010

Example 2: 47 base 10 to base 2

Think about the powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256,…

The highest power of 2 that is less than or equal to 47 is 2^5 = 32

To decompose 50 into sum of powers of 2, we need a 32 (2^5).  This would leave 15 (47 -32).

The highest power of 2 that is less than or equal to 15 is 2^3 = 8.  This would leave 7 (47 – 32 – 8).

The highest power of 2 that is less than or equal to 7 is 2^2 = 4.  This would leave 3. (47 – 32 – 8 – 4)

The highest power of 2 that is less than or equal to 3 is 2^1 = 2.  This would leave 1. (47 – 32 – 8 – 4 - 2)

The highest power of 2 that is less than or equal to 1 is 2^0 = 1.  This would leave 0.

47= 1*2^5 + 0*2^4 + 1*2^3 + 1*2^2 + 1*2^1 + 1*2^0.

47 base 10 can be written as follows in binary: 101111

Project 95: Variable 'decimal' has been initialized.  A working method called intDivision is available.

decimal is a positive integer between 5 and 250.

intDivision(x,y) returns how many times y can go into x.

intDivision(15,5) returns 3

intDivision(19,5) returns 3

Task: Appropriately assign the value of an array called 'bi' that represents the binary equivalent of 'decimal'.  

Example: if decimal = 47, bi should be [1,0,1,1,1,1] (as explained above)

Example: if decimal = 50, bi should be [1,1,0,0,1,0] (as explained above).

Note:  You can assume that 'bi' has already been assigned as an empty array (Javascript) or an empty ArrayList (Java)

**If your code works for 5 test cases, you can enter your e-mail address

Universal Computational Math Methods:

pow(5,2) returns 25.0

abs(-3.0) returns 3

sqrt(49.0) returns 7.0