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;
- 10 111 000 001 ÷ 2 = 5 055 500 000 + 1;
- 5 055 500 000 ÷ 2 = 2 527 750 000 + 0;
- 2 527 750 000 ÷ 2 = 1 263 875 000 + 0;
- 1 263 875 000 ÷ 2 = 631 937 500 + 0;
- 631 937 500 ÷ 2 = 315 968 750 + 0;
- 315 968 750 ÷ 2 = 157 984 375 + 0;
- 157 984 375 ÷ 2 = 78 992 187 + 1;
- 78 992 187 ÷ 2 = 39 496 093 + 1;
- 39 496 093 ÷ 2 = 19 748 046 + 1;
- 19 748 046 ÷ 2 = 9 874 023 + 0;
- 9 874 023 ÷ 2 = 4 937 011 + 1;
- 4 937 011 ÷ 2 = 2 468 505 + 1;
- 2 468 505 ÷ 2 = 1 234 252 + 1;
- 1 234 252 ÷ 2 = 617 126 + 0;
- 617 126 ÷ 2 = 308 563 + 0;
- 308 563 ÷ 2 = 154 281 + 1;
- 154 281 ÷ 2 = 77 140 + 1;
- 77 140 ÷ 2 = 38 570 + 0;
- 38 570 ÷ 2 = 19 285 + 0;
- 19 285 ÷ 2 = 9 642 + 1;
- 9 642 ÷ 2 = 4 821 + 0;
- 4 821 ÷ 2 = 2 410 + 1;
- 2 410 ÷ 2 = 1 205 + 0;
- 1 205 ÷ 2 = 602 + 1;
- 602 ÷ 2 = 301 + 0;
- 301 ÷ 2 = 150 + 1;
- 150 ÷ 2 = 75 + 0;
- 75 ÷ 2 = 37 + 1;
- 37 ÷ 2 = 18 + 1;
- 18 ÷ 2 = 9 + 0;
- 9 ÷ 2 = 4 + 1;
- 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.
10 111 000 001(10) = 10 0101 1010 1010 1001 1001 1101 1100 0001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 34.
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, 34,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 64.
4. Get the positive binary computer representation on 64 bits (8 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64:
Number 10 111 000 001(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
10 111 000 001(10) = 0000 0000 0000 0000 0000 0000 0000 0010 0101 1010 1010 1001 1001 1101 1100 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.