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;
- 4 582 748 776 ÷ 2 = 2 291 374 388 + 0;
- 2 291 374 388 ÷ 2 = 1 145 687 194 + 0;
- 1 145 687 194 ÷ 2 = 572 843 597 + 0;
- 572 843 597 ÷ 2 = 286 421 798 + 1;
- 286 421 798 ÷ 2 = 143 210 899 + 0;
- 143 210 899 ÷ 2 = 71 605 449 + 1;
- 71 605 449 ÷ 2 = 35 802 724 + 1;
- 35 802 724 ÷ 2 = 17 901 362 + 0;
- 17 901 362 ÷ 2 = 8 950 681 + 0;
- 8 950 681 ÷ 2 = 4 475 340 + 1;
- 4 475 340 ÷ 2 = 2 237 670 + 0;
- 2 237 670 ÷ 2 = 1 118 835 + 0;
- 1 118 835 ÷ 2 = 559 417 + 1;
- 559 417 ÷ 2 = 279 708 + 1;
- 279 708 ÷ 2 = 139 854 + 0;
- 139 854 ÷ 2 = 69 927 + 0;
- 69 927 ÷ 2 = 34 963 + 1;
- 34 963 ÷ 2 = 17 481 + 1;
- 17 481 ÷ 2 = 8 740 + 1;
- 8 740 ÷ 2 = 4 370 + 0;
- 4 370 ÷ 2 = 2 185 + 0;
- 2 185 ÷ 2 = 1 092 + 1;
- 1 092 ÷ 2 = 546 + 0;
- 546 ÷ 2 = 273 + 0;
- 273 ÷ 2 = 136 + 1;
- 136 ÷ 2 = 68 + 0;
- 68 ÷ 2 = 34 + 0;
- 34 ÷ 2 = 17 + 0;
- 17 ÷ 2 = 8 + 1;
- 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.
4 582 748 776(10) = 1 0001 0001 0010 0111 0011 0010 0110 1000(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 4 582 748 776(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
4 582 748 776(10) = 0000 0000 0000 0000 0000 0000 0000 0001 0001 0001 0010 0111 0011 0010 0110 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.