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;
- 2 341 652 ÷ 2 = 1 170 826 + 0;
- 1 170 826 ÷ 2 = 585 413 + 0;
- 585 413 ÷ 2 = 292 706 + 1;
- 292 706 ÷ 2 = 146 353 + 0;
- 146 353 ÷ 2 = 73 176 + 1;
- 73 176 ÷ 2 = 36 588 + 0;
- 36 588 ÷ 2 = 18 294 + 0;
- 18 294 ÷ 2 = 9 147 + 0;
- 9 147 ÷ 2 = 4 573 + 1;
- 4 573 ÷ 2 = 2 286 + 1;
- 2 286 ÷ 2 = 1 143 + 0;
- 1 143 ÷ 2 = 571 + 1;
- 571 ÷ 2 = 285 + 1;
- 285 ÷ 2 = 142 + 1;
- 142 ÷ 2 = 71 + 0;
- 71 ÷ 2 = 35 + 1;
- 35 ÷ 2 = 17 + 1;
- 17 ÷ 2 = 8 + 1;
- 8 ÷ 2 = 4 + 0;
- 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.
2 341 652(10) = 10 0011 1011 1011 0001 0100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 22.
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, 22,
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 2 341 652(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:
2 341 652(10) = 0000 0000 0010 0011 1011 1011 0001 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.