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;
- 1 230 366 356 ÷ 2 = 615 183 178 + 0;
- 615 183 178 ÷ 2 = 307 591 589 + 0;
- 307 591 589 ÷ 2 = 153 795 794 + 1;
- 153 795 794 ÷ 2 = 76 897 897 + 0;
- 76 897 897 ÷ 2 = 38 448 948 + 1;
- 38 448 948 ÷ 2 = 19 224 474 + 0;
- 19 224 474 ÷ 2 = 9 612 237 + 0;
- 9 612 237 ÷ 2 = 4 806 118 + 1;
- 4 806 118 ÷ 2 = 2 403 059 + 0;
- 2 403 059 ÷ 2 = 1 201 529 + 1;
- 1 201 529 ÷ 2 = 600 764 + 1;
- 600 764 ÷ 2 = 300 382 + 0;
- 300 382 ÷ 2 = 150 191 + 0;
- 150 191 ÷ 2 = 75 095 + 1;
- 75 095 ÷ 2 = 37 547 + 1;
- 37 547 ÷ 2 = 18 773 + 1;
- 18 773 ÷ 2 = 9 386 + 1;
- 9 386 ÷ 2 = 4 693 + 0;
- 4 693 ÷ 2 = 2 346 + 1;
- 2 346 ÷ 2 = 1 173 + 0;
- 1 173 ÷ 2 = 586 + 1;
- 586 ÷ 2 = 293 + 0;
- 293 ÷ 2 = 146 + 1;
- 146 ÷ 2 = 73 + 0;
- 73 ÷ 2 = 36 + 1;
- 36 ÷ 2 = 18 + 0;
- 18 ÷ 2 = 9 + 0;
- 9 ÷ 2 = 4 + 1;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 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.
1 230 366 356(10) = 100 1001 0101 0101 1110 0110 1001 0100(2)
3. 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.
4. 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:
Number 1 230 366 356(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
1 230 366 356(10) = 0100 1001 0101 0101 1110 0110 1001 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.