Convert the Positive Integer (Whole Number) 33 017 From Base Ten (10) To Base Two (2): Conversion and Writing of the Decimal System Number as an Unsigned Binary Code
Unsigned (positive) integer number 33 017(10)
converted and written as an unsigned binary (base 2) = ?
The steps we'll go through to make the conversion:
1. Divide the number repeatedly by 2
2. Construct the base 2 representation of the positive number
1. Divide the number repeatedly by 2:
Keep track of each remainder.
We stop when we get a quotient that is equal to zero.
- division = quotient + remainder;
- 33 017 ÷ 2 = 16 508 + 1;
- 16 508 ÷ 2 = 8 254 + 0;
- 8 254 ÷ 2 = 4 127 + 0;
- 4 127 ÷ 2 = 2 063 + 1;
- 2 063 ÷ 2 = 1 031 + 1;
- 1 031 ÷ 2 = 515 + 1;
- 515 ÷ 2 = 257 + 1;
- 257 ÷ 2 = 128 + 1;
- 128 ÷ 2 = 64 + 0;
- 64 ÷ 2 = 32 + 0;
- 32 ÷ 2 = 16 + 0;
- 16 ÷ 2 = 8 + 0;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 1 ÷ 2 = 0 + 1;
2. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
Number 33 017(10), a positive integer number (with no sign),
converted from decimal system (from base 10)
and written as an unsigned binary (in base 2):
33 017(10) = 1000 0000 1111 1001(2)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.
Convert positive integer numbers (unsigned) from decimal system (base ten) to binary (base two)
How to convert a base 10 positive integer number to base 2:
1) Divide the number repeatedly by 2, keeping track of each remainder, until getting a quotient that is 0;
2) Construct the base 2 representation by taking all the previously calculated remainders starting from the last remainder up to the first one, in that order.
The latest positive (unsigned) integer numbers converted from decimal system (written in base ten) to unsigned binary (written in base two)
How to convert unsigned integer numbers (positive) from decimal system (base 10) to binary = simply convert from base ten to base two
Follow the steps below to convert a base ten unsigned integer number to base two:
- 1. Divide repeatedly by 2 the positive integer number that has to be converted to binary, keeping track of each remainder, until we get a QUOTIENT that is equal to ZERO.
- 2. Construct the base 2 representation of the positive integer number, by taking all the remainders starting from the bottom of the list constructed above. Thus, the last remainder of the divisions becomes the first symbol (the leftmost) of the base two number, while the first remainder becomes the last symbol (the rightmost).
Example: convert the positive integer number 55 from decimal system (base ten) to binary code (base two):
- 1. Divide repeatedly 55 by 2, keeping track of each remainder, until we get a quotient that is equal to zero:
- division = quotient + remainder;
- 55 ÷ 2 = 27 + 1;
- 27 ÷ 2 = 13 + 1;
- 13 ÷ 2 = 6 + 1;
- 6 ÷ 2 = 3 + 0;
- 3 ÷ 2 = 1 + 1;
- 1 ÷ 2 = 0 + 1;
- 2. Construct the base 2 representation of the positive integer number, by taking all the remainders starting from the bottom of the list constructed above:
55(10) = 11 0111(2) -
Number 5510, positive integer (no sign), converted from decimal system (base 10) to unsigned binary (base 2) = 11 0111(2)
Available Base Conversions Between Decimal and Binary Systems
Conversions Between Decimal System Numbers (Written in Base Ten) and Binary System Numbers (Base Two and Computer Representation):
1. Integer -> Binary
2. Decimal -> Binary
3. Binary -> Integer
4. Binary -> Decimal