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;
- 23 786 420 ÷ 2 = 11 893 210 + 0;
- 11 893 210 ÷ 2 = 5 946 605 + 0;
- 5 946 605 ÷ 2 = 2 973 302 + 1;
- 2 973 302 ÷ 2 = 1 486 651 + 0;
- 1 486 651 ÷ 2 = 743 325 + 1;
- 743 325 ÷ 2 = 371 662 + 1;
- 371 662 ÷ 2 = 185 831 + 0;
- 185 831 ÷ 2 = 92 915 + 1;
- 92 915 ÷ 2 = 46 457 + 1;
- 46 457 ÷ 2 = 23 228 + 1;
- 23 228 ÷ 2 = 11 614 + 0;
- 11 614 ÷ 2 = 5 807 + 0;
- 5 807 ÷ 2 = 2 903 + 1;
- 2 903 ÷ 2 = 1 451 + 1;
- 1 451 ÷ 2 = 725 + 1;
- 725 ÷ 2 = 362 + 1;
- 362 ÷ 2 = 181 + 0;
- 181 ÷ 2 = 90 + 1;
- 90 ÷ 2 = 45 + 0;
- 45 ÷ 2 = 22 + 1;
- 22 ÷ 2 = 11 + 0;
- 11 ÷ 2 = 5 + 1;
- 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.
23 786 420(10) = 1 0110 1010 1111 0011 1011 0100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 25.
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, 25,
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 23 786 420(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:
23 786 420(10) = 0000 0001 0110 1010 1111 0011 1011 0100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.