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;
- 8 624 600 362 ÷ 2 = 4 312 300 181 + 0;
- 4 312 300 181 ÷ 2 = 2 156 150 090 + 1;
- 2 156 150 090 ÷ 2 = 1 078 075 045 + 0;
- 1 078 075 045 ÷ 2 = 539 037 522 + 1;
- 539 037 522 ÷ 2 = 269 518 761 + 0;
- 269 518 761 ÷ 2 = 134 759 380 + 1;
- 134 759 380 ÷ 2 = 67 379 690 + 0;
- 67 379 690 ÷ 2 = 33 689 845 + 0;
- 33 689 845 ÷ 2 = 16 844 922 + 1;
- 16 844 922 ÷ 2 = 8 422 461 + 0;
- 8 422 461 ÷ 2 = 4 211 230 + 1;
- 4 211 230 ÷ 2 = 2 105 615 + 0;
- 2 105 615 ÷ 2 = 1 052 807 + 1;
- 1 052 807 ÷ 2 = 526 403 + 1;
- 526 403 ÷ 2 = 263 201 + 1;
- 263 201 ÷ 2 = 131 600 + 1;
- 131 600 ÷ 2 = 65 800 + 0;
- 65 800 ÷ 2 = 32 900 + 0;
- 32 900 ÷ 2 = 16 450 + 0;
- 16 450 ÷ 2 = 8 225 + 0;
- 8 225 ÷ 2 = 4 112 + 1;
- 4 112 ÷ 2 = 2 056 + 0;
- 2 056 ÷ 2 = 1 028 + 0;
- 1 028 ÷ 2 = 514 + 0;
- 514 ÷ 2 = 257 + 0;
- 257 ÷ 2 = 128 + 1;
- 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.
8 624 600 362(10) = 10 0000 0010 0001 0000 1111 0101 0010 1010(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 8 624 600 362(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
8 624 600 362(10) = 0000 0000 0000 0000 0000 0000 0000 0010 0000 0010 0001 0000 1111 0101 0010 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.