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;
- 1 795 620 843 ÷ 2 = 897 810 421 + 1;
- 897 810 421 ÷ 2 = 448 905 210 + 1;
- 448 905 210 ÷ 2 = 224 452 605 + 0;
- 224 452 605 ÷ 2 = 112 226 302 + 1;
- 112 226 302 ÷ 2 = 56 113 151 + 0;
- 56 113 151 ÷ 2 = 28 056 575 + 1;
- 28 056 575 ÷ 2 = 14 028 287 + 1;
- 14 028 287 ÷ 2 = 7 014 143 + 1;
- 7 014 143 ÷ 2 = 3 507 071 + 1;
- 3 507 071 ÷ 2 = 1 753 535 + 1;
- 1 753 535 ÷ 2 = 876 767 + 1;
- 876 767 ÷ 2 = 438 383 + 1;
- 438 383 ÷ 2 = 219 191 + 1;
- 219 191 ÷ 2 = 109 595 + 1;
- 109 595 ÷ 2 = 54 797 + 1;
- 54 797 ÷ 2 = 27 398 + 1;
- 27 398 ÷ 2 = 13 699 + 0;
- 13 699 ÷ 2 = 6 849 + 1;
- 6 849 ÷ 2 = 3 424 + 1;
- 3 424 ÷ 2 = 1 712 + 0;
- 1 712 ÷ 2 = 856 + 0;
- 856 ÷ 2 = 428 + 0;
- 428 ÷ 2 = 214 + 0;
- 214 ÷ 2 = 107 + 0;
- 107 ÷ 2 = 53 + 1;
- 53 ÷ 2 = 26 + 1;
- 26 ÷ 2 = 13 + 0;
- 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.
1 795 620 843(10) = 110 1011 0000 0110 1111 1111 1110 1011(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:
1 795 620 843(10) = 0110 1011 0000 0110 1111 1111 1110 1011
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 -1 795 620 843(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-1 795 620 843(10) = 1110 1011 0000 0110 1111 1111 1110 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.