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;
- 156 624 483 ÷ 2 = 78 312 241 + 1;
- 78 312 241 ÷ 2 = 39 156 120 + 1;
- 39 156 120 ÷ 2 = 19 578 060 + 0;
- 19 578 060 ÷ 2 = 9 789 030 + 0;
- 9 789 030 ÷ 2 = 4 894 515 + 0;
- 4 894 515 ÷ 2 = 2 447 257 + 1;
- 2 447 257 ÷ 2 = 1 223 628 + 1;
- 1 223 628 ÷ 2 = 611 814 + 0;
- 611 814 ÷ 2 = 305 907 + 0;
- 305 907 ÷ 2 = 152 953 + 1;
- 152 953 ÷ 2 = 76 476 + 1;
- 76 476 ÷ 2 = 38 238 + 0;
- 38 238 ÷ 2 = 19 119 + 0;
- 19 119 ÷ 2 = 9 559 + 1;
- 9 559 ÷ 2 = 4 779 + 1;
- 4 779 ÷ 2 = 2 389 + 1;
- 2 389 ÷ 2 = 1 194 + 1;
- 1 194 ÷ 2 = 597 + 0;
- 597 ÷ 2 = 298 + 1;
- 298 ÷ 2 = 149 + 0;
- 149 ÷ 2 = 74 + 1;
- 74 ÷ 2 = 37 + 0;
- 37 ÷ 2 = 18 + 1;
- 18 ÷ 2 = 9 + 0;
- 9 ÷ 2 = 4 + 1;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 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.
156 624 483(10) = 1001 0101 0101 1110 0110 0110 0011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 28.
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, 28,
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 156 624 483(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:
156 624 483(10) = 0000 1001 0101 0101 1110 0110 0110 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.