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;
- 1 361 143 ÷ 2 = 680 571 + 1;
- 680 571 ÷ 2 = 340 285 + 1;
- 340 285 ÷ 2 = 170 142 + 1;
- 170 142 ÷ 2 = 85 071 + 0;
- 85 071 ÷ 2 = 42 535 + 1;
- 42 535 ÷ 2 = 21 267 + 1;
- 21 267 ÷ 2 = 10 633 + 1;
- 10 633 ÷ 2 = 5 316 + 1;
- 5 316 ÷ 2 = 2 658 + 0;
- 2 658 ÷ 2 = 1 329 + 0;
- 1 329 ÷ 2 = 664 + 1;
- 664 ÷ 2 = 332 + 0;
- 332 ÷ 2 = 166 + 0;
- 166 ÷ 2 = 83 + 0;
- 83 ÷ 2 = 41 + 1;
- 41 ÷ 2 = 20 + 1;
- 20 ÷ 2 = 10 + 0;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 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.
1 361 143(10) = 1 0100 1100 0100 1111 0111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 21.
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, 21,
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 1 361 143(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:
1 361 143(10) = 0000 0000 0001 0100 1100 0100 1111 0111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.