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;
- 4 286 578 696 ÷ 2 = 2 143 289 348 + 0;
- 2 143 289 348 ÷ 2 = 1 071 644 674 + 0;
- 1 071 644 674 ÷ 2 = 535 822 337 + 0;
- 535 822 337 ÷ 2 = 267 911 168 + 1;
- 267 911 168 ÷ 2 = 133 955 584 + 0;
- 133 955 584 ÷ 2 = 66 977 792 + 0;
- 66 977 792 ÷ 2 = 33 488 896 + 0;
- 33 488 896 ÷ 2 = 16 744 448 + 0;
- 16 744 448 ÷ 2 = 8 372 224 + 0;
- 8 372 224 ÷ 2 = 4 186 112 + 0;
- 4 186 112 ÷ 2 = 2 093 056 + 0;
- 2 093 056 ÷ 2 = 1 046 528 + 0;
- 1 046 528 ÷ 2 = 523 264 + 0;
- 523 264 ÷ 2 = 261 632 + 0;
- 261 632 ÷ 2 = 130 816 + 0;
- 130 816 ÷ 2 = 65 408 + 0;
- 65 408 ÷ 2 = 32 704 + 0;
- 32 704 ÷ 2 = 16 352 + 0;
- 16 352 ÷ 2 = 8 176 + 0;
- 8 176 ÷ 2 = 4 088 + 0;
- 4 088 ÷ 2 = 2 044 + 0;
- 2 044 ÷ 2 = 1 022 + 0;
- 1 022 ÷ 2 = 511 + 0;
- 511 ÷ 2 = 255 + 1;
- 255 ÷ 2 = 127 + 1;
- 127 ÷ 2 = 63 + 1;
- 63 ÷ 2 = 31 + 1;
- 31 ÷ 2 = 15 + 1;
- 15 ÷ 2 = 7 + 1;
- 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.
4 286 578 696(10) = 1111 1111 1000 0000 0000 0000 0000 1000(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) 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, 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 4 286 578 696(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:
4 286 578 696(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1111 1111 1000 0000 0000 0000 0000 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.