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;
- 3 263 594 482 ÷ 2 = 1 631 797 241 + 0;
- 1 631 797 241 ÷ 2 = 815 898 620 + 1;
- 815 898 620 ÷ 2 = 407 949 310 + 0;
- 407 949 310 ÷ 2 = 203 974 655 + 0;
- 203 974 655 ÷ 2 = 101 987 327 + 1;
- 101 987 327 ÷ 2 = 50 993 663 + 1;
- 50 993 663 ÷ 2 = 25 496 831 + 1;
- 25 496 831 ÷ 2 = 12 748 415 + 1;
- 12 748 415 ÷ 2 = 6 374 207 + 1;
- 6 374 207 ÷ 2 = 3 187 103 + 1;
- 3 187 103 ÷ 2 = 1 593 551 + 1;
- 1 593 551 ÷ 2 = 796 775 + 1;
- 796 775 ÷ 2 = 398 387 + 1;
- 398 387 ÷ 2 = 199 193 + 1;
- 199 193 ÷ 2 = 99 596 + 1;
- 99 596 ÷ 2 = 49 798 + 0;
- 49 798 ÷ 2 = 24 899 + 0;
- 24 899 ÷ 2 = 12 449 + 1;
- 12 449 ÷ 2 = 6 224 + 1;
- 6 224 ÷ 2 = 3 112 + 0;
- 3 112 ÷ 2 = 1 556 + 0;
- 1 556 ÷ 2 = 778 + 0;
- 778 ÷ 2 = 389 + 0;
- 389 ÷ 2 = 194 + 1;
- 194 ÷ 2 = 97 + 0;
- 97 ÷ 2 = 48 + 1;
- 48 ÷ 2 = 24 + 0;
- 24 ÷ 2 = 12 + 0;
- 12 ÷ 2 = 6 + 0;
- 6 ÷ 2 = 3 + 0;
- 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.
3 263 594 482(10) = 1100 0010 1000 0110 0111 1111 1111 0010(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 3 263 594 482(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:
3 263 594 482(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1100 0010 1000 0110 0111 1111 1111 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.