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;
- 1 904 803 927 ÷ 2 = 952 401 963 + 1;
- 952 401 963 ÷ 2 = 476 200 981 + 1;
- 476 200 981 ÷ 2 = 238 100 490 + 1;
- 238 100 490 ÷ 2 = 119 050 245 + 0;
- 119 050 245 ÷ 2 = 59 525 122 + 1;
- 59 525 122 ÷ 2 = 29 762 561 + 0;
- 29 762 561 ÷ 2 = 14 881 280 + 1;
- 14 881 280 ÷ 2 = 7 440 640 + 0;
- 7 440 640 ÷ 2 = 3 720 320 + 0;
- 3 720 320 ÷ 2 = 1 860 160 + 0;
- 1 860 160 ÷ 2 = 930 080 + 0;
- 930 080 ÷ 2 = 465 040 + 0;
- 465 040 ÷ 2 = 232 520 + 0;
- 232 520 ÷ 2 = 116 260 + 0;
- 116 260 ÷ 2 = 58 130 + 0;
- 58 130 ÷ 2 = 29 065 + 0;
- 29 065 ÷ 2 = 14 532 + 1;
- 14 532 ÷ 2 = 7 266 + 0;
- 7 266 ÷ 2 = 3 633 + 0;
- 3 633 ÷ 2 = 1 816 + 1;
- 1 816 ÷ 2 = 908 + 0;
- 908 ÷ 2 = 454 + 0;
- 454 ÷ 2 = 227 + 0;
- 227 ÷ 2 = 113 + 1;
- 113 ÷ 2 = 56 + 1;
- 56 ÷ 2 = 28 + 0;
- 28 ÷ 2 = 14 + 0;
- 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.
1 904 803 927(10) = 111 0001 1000 1001 0000 0000 0101 0111(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) indicates 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 1 904 803 927(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
1 904 803 927(10) = 0111 0001 1000 1001 0000 0000 0101 0111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.