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;
- 253 706 111 ÷ 2 = 126 853 055 + 1;
- 126 853 055 ÷ 2 = 63 426 527 + 1;
- 63 426 527 ÷ 2 = 31 713 263 + 1;
- 31 713 263 ÷ 2 = 15 856 631 + 1;
- 15 856 631 ÷ 2 = 7 928 315 + 1;
- 7 928 315 ÷ 2 = 3 964 157 + 1;
- 3 964 157 ÷ 2 = 1 982 078 + 1;
- 1 982 078 ÷ 2 = 991 039 + 0;
- 991 039 ÷ 2 = 495 519 + 1;
- 495 519 ÷ 2 = 247 759 + 1;
- 247 759 ÷ 2 = 123 879 + 1;
- 123 879 ÷ 2 = 61 939 + 1;
- 61 939 ÷ 2 = 30 969 + 1;
- 30 969 ÷ 2 = 15 484 + 1;
- 15 484 ÷ 2 = 7 742 + 0;
- 7 742 ÷ 2 = 3 871 + 0;
- 3 871 ÷ 2 = 1 935 + 1;
- 1 935 ÷ 2 = 967 + 1;
- 967 ÷ 2 = 483 + 1;
- 483 ÷ 2 = 241 + 1;
- 241 ÷ 2 = 120 + 1;
- 120 ÷ 2 = 60 + 0;
- 60 ÷ 2 = 30 + 0;
- 30 ÷ 2 = 15 + 0;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 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.
253 706 111(10) = 1111 0001 1111 0011 1111 0111 1111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 28.
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, 28,
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 253 706 111(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
253 706 111(10) = 0000 1111 0001 1111 0011 1111 0111 1111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.