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;
- 1 000 120 987 ÷ 2 = 500 060 493 + 1;
- 500 060 493 ÷ 2 = 250 030 246 + 1;
- 250 030 246 ÷ 2 = 125 015 123 + 0;
- 125 015 123 ÷ 2 = 62 507 561 + 1;
- 62 507 561 ÷ 2 = 31 253 780 + 1;
- 31 253 780 ÷ 2 = 15 626 890 + 0;
- 15 626 890 ÷ 2 = 7 813 445 + 0;
- 7 813 445 ÷ 2 = 3 906 722 + 1;
- 3 906 722 ÷ 2 = 1 953 361 + 0;
- 1 953 361 ÷ 2 = 976 680 + 1;
- 976 680 ÷ 2 = 488 340 + 0;
- 488 340 ÷ 2 = 244 170 + 0;
- 244 170 ÷ 2 = 122 085 + 0;
- 122 085 ÷ 2 = 61 042 + 1;
- 61 042 ÷ 2 = 30 521 + 0;
- 30 521 ÷ 2 = 15 260 + 1;
- 15 260 ÷ 2 = 7 630 + 0;
- 7 630 ÷ 2 = 3 815 + 0;
- 3 815 ÷ 2 = 1 907 + 1;
- 1 907 ÷ 2 = 953 + 1;
- 953 ÷ 2 = 476 + 1;
- 476 ÷ 2 = 238 + 0;
- 238 ÷ 2 = 119 + 0;
- 119 ÷ 2 = 59 + 1;
- 59 ÷ 2 = 29 + 1;
- 29 ÷ 2 = 14 + 1;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 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.
1 000 120 987(10) = 11 1011 1001 1100 1010 0010 1001 1011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 30.
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, 30,
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 1 000 120 987(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
1 000 120 987(10) = 0011 1011 1001 1100 1010 0010 1001 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.