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;
- 111 109 992 ÷ 2 = 55 554 996 + 0;
- 55 554 996 ÷ 2 = 27 777 498 + 0;
- 27 777 498 ÷ 2 = 13 888 749 + 0;
- 13 888 749 ÷ 2 = 6 944 374 + 1;
- 6 944 374 ÷ 2 = 3 472 187 + 0;
- 3 472 187 ÷ 2 = 1 736 093 + 1;
- 1 736 093 ÷ 2 = 868 046 + 1;
- 868 046 ÷ 2 = 434 023 + 0;
- 434 023 ÷ 2 = 217 011 + 1;
- 217 011 ÷ 2 = 108 505 + 1;
- 108 505 ÷ 2 = 54 252 + 1;
- 54 252 ÷ 2 = 27 126 + 0;
- 27 126 ÷ 2 = 13 563 + 0;
- 13 563 ÷ 2 = 6 781 + 1;
- 6 781 ÷ 2 = 3 390 + 1;
- 3 390 ÷ 2 = 1 695 + 0;
- 1 695 ÷ 2 = 847 + 1;
- 847 ÷ 2 = 423 + 1;
- 423 ÷ 2 = 211 + 1;
- 211 ÷ 2 = 105 + 1;
- 105 ÷ 2 = 52 + 1;
- 52 ÷ 2 = 26 + 0;
- 26 ÷ 2 = 13 + 0;
- 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.
111 109 992(10) = 110 1001 1111 0110 0111 0110 1000(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 111 109 992(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:
111 109 992(10) = 0000 0110 1001 1111 0110 0111 0110 1000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.