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;
- 110 011 116 ÷ 2 = 55 005 558 + 0;
- 55 005 558 ÷ 2 = 27 502 779 + 0;
- 27 502 779 ÷ 2 = 13 751 389 + 1;
- 13 751 389 ÷ 2 = 6 875 694 + 1;
- 6 875 694 ÷ 2 = 3 437 847 + 0;
- 3 437 847 ÷ 2 = 1 718 923 + 1;
- 1 718 923 ÷ 2 = 859 461 + 1;
- 859 461 ÷ 2 = 429 730 + 1;
- 429 730 ÷ 2 = 214 865 + 0;
- 214 865 ÷ 2 = 107 432 + 1;
- 107 432 ÷ 2 = 53 716 + 0;
- 53 716 ÷ 2 = 26 858 + 0;
- 26 858 ÷ 2 = 13 429 + 0;
- 13 429 ÷ 2 = 6 714 + 1;
- 6 714 ÷ 2 = 3 357 + 0;
- 3 357 ÷ 2 = 1 678 + 1;
- 1 678 ÷ 2 = 839 + 0;
- 839 ÷ 2 = 419 + 1;
- 419 ÷ 2 = 209 + 1;
- 209 ÷ 2 = 104 + 1;
- 104 ÷ 2 = 52 + 0;
- 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.
110 011 116(10) = 110 1000 1110 1010 0010 1110 1100(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 110 011 116(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:
110 011 116(10) = 0000 0110 1000 1110 1010 0010 1110 1100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.