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;
- 101 100 858 ÷ 2 = 50 550 429 + 0;
- 50 550 429 ÷ 2 = 25 275 214 + 1;
- 25 275 214 ÷ 2 = 12 637 607 + 0;
- 12 637 607 ÷ 2 = 6 318 803 + 1;
- 6 318 803 ÷ 2 = 3 159 401 + 1;
- 3 159 401 ÷ 2 = 1 579 700 + 1;
- 1 579 700 ÷ 2 = 789 850 + 0;
- 789 850 ÷ 2 = 394 925 + 0;
- 394 925 ÷ 2 = 197 462 + 1;
- 197 462 ÷ 2 = 98 731 + 0;
- 98 731 ÷ 2 = 49 365 + 1;
- 49 365 ÷ 2 = 24 682 + 1;
- 24 682 ÷ 2 = 12 341 + 0;
- 12 341 ÷ 2 = 6 170 + 1;
- 6 170 ÷ 2 = 3 085 + 0;
- 3 085 ÷ 2 = 1 542 + 1;
- 1 542 ÷ 2 = 771 + 0;
- 771 ÷ 2 = 385 + 1;
- 385 ÷ 2 = 192 + 1;
- 192 ÷ 2 = 96 + 0;
- 96 ÷ 2 = 48 + 0;
- 48 ÷ 2 = 24 + 0;
- 24 ÷ 2 = 12 + 0;
- 12 ÷ 2 = 6 + 0;
- 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.
101 100 858(10) = 110 0000 0110 1010 1101 0011 1010(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 101 100 858(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:
101 100 858(10) = 0000 0110 0000 0110 1010 1101 0011 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.