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;
- 116 711 842 ÷ 2 = 58 355 921 + 0;
- 58 355 921 ÷ 2 = 29 177 960 + 1;
- 29 177 960 ÷ 2 = 14 588 980 + 0;
- 14 588 980 ÷ 2 = 7 294 490 + 0;
- 7 294 490 ÷ 2 = 3 647 245 + 0;
- 3 647 245 ÷ 2 = 1 823 622 + 1;
- 1 823 622 ÷ 2 = 911 811 + 0;
- 911 811 ÷ 2 = 455 905 + 1;
- 455 905 ÷ 2 = 227 952 + 1;
- 227 952 ÷ 2 = 113 976 + 0;
- 113 976 ÷ 2 = 56 988 + 0;
- 56 988 ÷ 2 = 28 494 + 0;
- 28 494 ÷ 2 = 14 247 + 0;
- 14 247 ÷ 2 = 7 123 + 1;
- 7 123 ÷ 2 = 3 561 + 1;
- 3 561 ÷ 2 = 1 780 + 1;
- 1 780 ÷ 2 = 890 + 0;
- 890 ÷ 2 = 445 + 0;
- 445 ÷ 2 = 222 + 1;
- 222 ÷ 2 = 111 + 0;
- 111 ÷ 2 = 55 + 1;
- 55 ÷ 2 = 27 + 1;
- 27 ÷ 2 = 13 + 1;
- 13 ÷ 2 = 6 + 1;
- 6 ÷ 2 = 3 + 0;
- 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.
116 711 842(10) = 110 1111 0100 1110 0001 1010 0010(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 27.
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, 27,
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 116 711 842(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
116 711 842(10) = 0000 0110 1111 0100 1110 0001 1010 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.