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;
- 2 131 822 000 ÷ 2 = 1 065 911 000 + 0;
- 1 065 911 000 ÷ 2 = 532 955 500 + 0;
- 532 955 500 ÷ 2 = 266 477 750 + 0;
- 266 477 750 ÷ 2 = 133 238 875 + 0;
- 133 238 875 ÷ 2 = 66 619 437 + 1;
- 66 619 437 ÷ 2 = 33 309 718 + 1;
- 33 309 718 ÷ 2 = 16 654 859 + 0;
- 16 654 859 ÷ 2 = 8 327 429 + 1;
- 8 327 429 ÷ 2 = 4 163 714 + 1;
- 4 163 714 ÷ 2 = 2 081 857 + 0;
- 2 081 857 ÷ 2 = 1 040 928 + 1;
- 1 040 928 ÷ 2 = 520 464 + 0;
- 520 464 ÷ 2 = 260 232 + 0;
- 260 232 ÷ 2 = 130 116 + 0;
- 130 116 ÷ 2 = 65 058 + 0;
- 65 058 ÷ 2 = 32 529 + 0;
- 32 529 ÷ 2 = 16 264 + 1;
- 16 264 ÷ 2 = 8 132 + 0;
- 8 132 ÷ 2 = 4 066 + 0;
- 4 066 ÷ 2 = 2 033 + 0;
- 2 033 ÷ 2 = 1 016 + 1;
- 1 016 ÷ 2 = 508 + 0;
- 508 ÷ 2 = 254 + 0;
- 254 ÷ 2 = 127 + 0;
- 127 ÷ 2 = 63 + 1;
- 63 ÷ 2 = 31 + 1;
- 31 ÷ 2 = 15 + 1;
- 15 ÷ 2 = 7 + 1;
- 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.
2 131 822 000(10) = 111 1111 0001 0001 0000 0101 1011 0000(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 2 131 822 000(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
2 131 822 000(10) = 0111 1111 0001 0001 0000 0101 1011 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.