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;
- 7 635 497 430 ÷ 2 = 3 817 748 715 + 0;
- 3 817 748 715 ÷ 2 = 1 908 874 357 + 1;
- 1 908 874 357 ÷ 2 = 954 437 178 + 1;
- 954 437 178 ÷ 2 = 477 218 589 + 0;
- 477 218 589 ÷ 2 = 238 609 294 + 1;
- 238 609 294 ÷ 2 = 119 304 647 + 0;
- 119 304 647 ÷ 2 = 59 652 323 + 1;
- 59 652 323 ÷ 2 = 29 826 161 + 1;
- 29 826 161 ÷ 2 = 14 913 080 + 1;
- 14 913 080 ÷ 2 = 7 456 540 + 0;
- 7 456 540 ÷ 2 = 3 728 270 + 0;
- 3 728 270 ÷ 2 = 1 864 135 + 0;
- 1 864 135 ÷ 2 = 932 067 + 1;
- 932 067 ÷ 2 = 466 033 + 1;
- 466 033 ÷ 2 = 233 016 + 1;
- 233 016 ÷ 2 = 116 508 + 0;
- 116 508 ÷ 2 = 58 254 + 0;
- 58 254 ÷ 2 = 29 127 + 0;
- 29 127 ÷ 2 = 14 563 + 1;
- 14 563 ÷ 2 = 7 281 + 1;
- 7 281 ÷ 2 = 3 640 + 1;
- 3 640 ÷ 2 = 1 820 + 0;
- 1 820 ÷ 2 = 910 + 0;
- 910 ÷ 2 = 455 + 0;
- 455 ÷ 2 = 227 + 1;
- 227 ÷ 2 = 113 + 1;
- 113 ÷ 2 = 56 + 1;
- 56 ÷ 2 = 28 + 0;
- 28 ÷ 2 = 14 + 0;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 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.
7 635 497 430(10) = 1 1100 0111 0001 1100 0111 0001 1101 0110(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) indicates 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 7 635 497 430(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
7 635 497 430(10) = 0000 0000 0000 0000 0000 0000 0000 0001 1100 0111 0001 1100 0111 0001 1101 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.