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;
- 3 147 483 652 ÷ 2 = 1 573 741 826 + 0;
- 1 573 741 826 ÷ 2 = 786 870 913 + 0;
- 786 870 913 ÷ 2 = 393 435 456 + 1;
- 393 435 456 ÷ 2 = 196 717 728 + 0;
- 196 717 728 ÷ 2 = 98 358 864 + 0;
- 98 358 864 ÷ 2 = 49 179 432 + 0;
- 49 179 432 ÷ 2 = 24 589 716 + 0;
- 24 589 716 ÷ 2 = 12 294 858 + 0;
- 12 294 858 ÷ 2 = 6 147 429 + 0;
- 6 147 429 ÷ 2 = 3 073 714 + 1;
- 3 073 714 ÷ 2 = 1 536 857 + 0;
- 1 536 857 ÷ 2 = 768 428 + 1;
- 768 428 ÷ 2 = 384 214 + 0;
- 384 214 ÷ 2 = 192 107 + 0;
- 192 107 ÷ 2 = 96 053 + 1;
- 96 053 ÷ 2 = 48 026 + 1;
- 48 026 ÷ 2 = 24 013 + 0;
- 24 013 ÷ 2 = 12 006 + 1;
- 12 006 ÷ 2 = 6 003 + 0;
- 6 003 ÷ 2 = 3 001 + 1;
- 3 001 ÷ 2 = 1 500 + 1;
- 1 500 ÷ 2 = 750 + 0;
- 750 ÷ 2 = 375 + 0;
- 375 ÷ 2 = 187 + 1;
- 187 ÷ 2 = 93 + 1;
- 93 ÷ 2 = 46 + 1;
- 46 ÷ 2 = 23 + 0;
- 23 ÷ 2 = 11 + 1;
- 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.
3 147 483 652(10) = 1011 1011 1001 1010 1100 1010 0000 0100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 32.
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, 32,
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 3 147 483 652(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
3 147 483 652(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1011 1011 1001 1010 1100 1010 0000 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.