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;
- 28 101 968 ÷ 2 = 14 050 984 + 0;
- 14 050 984 ÷ 2 = 7 025 492 + 0;
- 7 025 492 ÷ 2 = 3 512 746 + 0;
- 3 512 746 ÷ 2 = 1 756 373 + 0;
- 1 756 373 ÷ 2 = 878 186 + 1;
- 878 186 ÷ 2 = 439 093 + 0;
- 439 093 ÷ 2 = 219 546 + 1;
- 219 546 ÷ 2 = 109 773 + 0;
- 109 773 ÷ 2 = 54 886 + 1;
- 54 886 ÷ 2 = 27 443 + 0;
- 27 443 ÷ 2 = 13 721 + 1;
- 13 721 ÷ 2 = 6 860 + 1;
- 6 860 ÷ 2 = 3 430 + 0;
- 3 430 ÷ 2 = 1 715 + 0;
- 1 715 ÷ 2 = 857 + 1;
- 857 ÷ 2 = 428 + 1;
- 428 ÷ 2 = 214 + 0;
- 214 ÷ 2 = 107 + 0;
- 107 ÷ 2 = 53 + 1;
- 53 ÷ 2 = 26 + 1;
- 26 ÷ 2 = 13 + 0;
- 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 number:
Take all the remainders starting from the bottom of the list constructed above.
28 101 968(10) = 1 1010 1100 1100 1101 0101 0000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 25.
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, 25,
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 28 101 968(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
28 101 968(10) = 0000 0001 1010 1100 1100 1101 0101 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.