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;
- 4 303 364 388 ÷ 2 = 2 151 682 194 + 0;
- 2 151 682 194 ÷ 2 = 1 075 841 097 + 0;
- 1 075 841 097 ÷ 2 = 537 920 548 + 1;
- 537 920 548 ÷ 2 = 268 960 274 + 0;
- 268 960 274 ÷ 2 = 134 480 137 + 0;
- 134 480 137 ÷ 2 = 67 240 068 + 1;
- 67 240 068 ÷ 2 = 33 620 034 + 0;
- 33 620 034 ÷ 2 = 16 810 017 + 0;
- 16 810 017 ÷ 2 = 8 405 008 + 1;
- 8 405 008 ÷ 2 = 4 202 504 + 0;
- 4 202 504 ÷ 2 = 2 101 252 + 0;
- 2 101 252 ÷ 2 = 1 050 626 + 0;
- 1 050 626 ÷ 2 = 525 313 + 0;
- 525 313 ÷ 2 = 262 656 + 1;
- 262 656 ÷ 2 = 131 328 + 0;
- 131 328 ÷ 2 = 65 664 + 0;
- 65 664 ÷ 2 = 32 832 + 0;
- 32 832 ÷ 2 = 16 416 + 0;
- 16 416 ÷ 2 = 8 208 + 0;
- 8 208 ÷ 2 = 4 104 + 0;
- 4 104 ÷ 2 = 2 052 + 0;
- 2 052 ÷ 2 = 1 026 + 0;
- 1 026 ÷ 2 = 513 + 0;
- 513 ÷ 2 = 256 + 1;
- 256 ÷ 2 = 128 + 0;
- 128 ÷ 2 = 64 + 0;
- 64 ÷ 2 = 32 + 0;
- 32 ÷ 2 = 16 + 0;
- 16 ÷ 2 = 8 + 0;
- 8 ÷ 2 = 4 + 0;
- 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.
4 303 364 388(10) = 1 0000 0000 1000 0000 0010 0001 0010 0100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 33.
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, 33,
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 4 303 364 388(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
4 303 364 388(10) = 0000 0000 0000 0000 0000 0000 0000 0001 0000 0000 1000 0000 0010 0001 0010 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.