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;
- 6 020 250 ÷ 2 = 3 010 125 + 0;
- 3 010 125 ÷ 2 = 1 505 062 + 1;
- 1 505 062 ÷ 2 = 752 531 + 0;
- 752 531 ÷ 2 = 376 265 + 1;
- 376 265 ÷ 2 = 188 132 + 1;
- 188 132 ÷ 2 = 94 066 + 0;
- 94 066 ÷ 2 = 47 033 + 0;
- 47 033 ÷ 2 = 23 516 + 1;
- 23 516 ÷ 2 = 11 758 + 0;
- 11 758 ÷ 2 = 5 879 + 0;
- 5 879 ÷ 2 = 2 939 + 1;
- 2 939 ÷ 2 = 1 469 + 1;
- 1 469 ÷ 2 = 734 + 1;
- 734 ÷ 2 = 367 + 0;
- 367 ÷ 2 = 183 + 1;
- 183 ÷ 2 = 91 + 1;
- 91 ÷ 2 = 45 + 1;
- 45 ÷ 2 = 22 + 1;
- 22 ÷ 2 = 11 + 0;
- 11 ÷ 2 = 5 + 1;
- 5 ÷ 2 = 2 + 1;
- 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.
6 020 250(10) = 101 1011 1101 1100 1001 1010(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 23.
A signed binary's bit length must be equal to a power of 2, as of:
21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
The first bit (the leftmost) is reserved for the sign:
0 = positive integer number, 1 = negative integer number
The least number that is:
1) a power of 2
2) and is larger than the actual length, 23,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
4. Get the positive binary computer representation on 32 bits (4 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32:
Number 6 020 250(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
6 020 250(10) = 0000 0000 0101 1011 1101 1100 1001 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.