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;
- 3 352 949 556 ÷ 2 = 1 676 474 778 + 0;
- 1 676 474 778 ÷ 2 = 838 237 389 + 0;
- 838 237 389 ÷ 2 = 419 118 694 + 1;
- 419 118 694 ÷ 2 = 209 559 347 + 0;
- 209 559 347 ÷ 2 = 104 779 673 + 1;
- 104 779 673 ÷ 2 = 52 389 836 + 1;
- 52 389 836 ÷ 2 = 26 194 918 + 0;
- 26 194 918 ÷ 2 = 13 097 459 + 0;
- 13 097 459 ÷ 2 = 6 548 729 + 1;
- 6 548 729 ÷ 2 = 3 274 364 + 1;
- 3 274 364 ÷ 2 = 1 637 182 + 0;
- 1 637 182 ÷ 2 = 818 591 + 0;
- 818 591 ÷ 2 = 409 295 + 1;
- 409 295 ÷ 2 = 204 647 + 1;
- 204 647 ÷ 2 = 102 323 + 1;
- 102 323 ÷ 2 = 51 161 + 1;
- 51 161 ÷ 2 = 25 580 + 1;
- 25 580 ÷ 2 = 12 790 + 0;
- 12 790 ÷ 2 = 6 395 + 0;
- 6 395 ÷ 2 = 3 197 + 1;
- 3 197 ÷ 2 = 1 598 + 1;
- 1 598 ÷ 2 = 799 + 0;
- 799 ÷ 2 = 399 + 1;
- 399 ÷ 2 = 199 + 1;
- 199 ÷ 2 = 99 + 1;
- 99 ÷ 2 = 49 + 1;
- 49 ÷ 2 = 24 + 1;
- 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.
3 352 949 556(10) = 1100 0111 1101 1001 1111 0011 0011 0100(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 3 352 949 556(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:
3 352 949 556(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1100 0111 1101 1001 1111 0011 0011 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.