2. 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;
- 1 836 530 430 ÷ 2 = 918 265 215 + 0;
- 918 265 215 ÷ 2 = 459 132 607 + 1;
- 459 132 607 ÷ 2 = 229 566 303 + 1;
- 229 566 303 ÷ 2 = 114 783 151 + 1;
- 114 783 151 ÷ 2 = 57 391 575 + 1;
- 57 391 575 ÷ 2 = 28 695 787 + 1;
- 28 695 787 ÷ 2 = 14 347 893 + 1;
- 14 347 893 ÷ 2 = 7 173 946 + 1;
- 7 173 946 ÷ 2 = 3 586 973 + 0;
- 3 586 973 ÷ 2 = 1 793 486 + 1;
- 1 793 486 ÷ 2 = 896 743 + 0;
- 896 743 ÷ 2 = 448 371 + 1;
- 448 371 ÷ 2 = 224 185 + 1;
- 224 185 ÷ 2 = 112 092 + 1;
- 112 092 ÷ 2 = 56 046 + 0;
- 56 046 ÷ 2 = 28 023 + 0;
- 28 023 ÷ 2 = 14 011 + 1;
- 14 011 ÷ 2 = 7 005 + 1;
- 7 005 ÷ 2 = 3 502 + 1;
- 3 502 ÷ 2 = 1 751 + 0;
- 1 751 ÷ 2 = 875 + 1;
- 875 ÷ 2 = 437 + 1;
- 437 ÷ 2 = 218 + 1;
- 218 ÷ 2 = 109 + 0;
- 109 ÷ 2 = 54 + 1;
- 54 ÷ 2 = 27 + 0;
- 27 ÷ 2 = 13 + 1;
- 13 ÷ 2 = 6 + 1;
- 6 ÷ 2 = 3 + 0;
- 3 ÷ 2 = 1 + 1;
- 1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
1 836 530 430(10) = 110 1101 0111 0111 0011 1010 1111 1110(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 31.
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, 31,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
5. Get the positive binary computer representation on 32 bits (4 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 32:
1 836 530 430(10) = 0110 1101 0111 0111 0011 1010 1111 1110
6. Get the negative integer number representation:
To get the negative integer number representation on 32 bits (4 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -1 836 530 430(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-1 836 530 430(10) = 1110 1101 0111 0111 0011 1010 1111 1110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.