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;
- 3 850 019 ÷ 2 = 1 925 009 + 1;
- 1 925 009 ÷ 2 = 962 504 + 1;
- 962 504 ÷ 2 = 481 252 + 0;
- 481 252 ÷ 2 = 240 626 + 0;
- 240 626 ÷ 2 = 120 313 + 0;
- 120 313 ÷ 2 = 60 156 + 1;
- 60 156 ÷ 2 = 30 078 + 0;
- 30 078 ÷ 2 = 15 039 + 0;
- 15 039 ÷ 2 = 7 519 + 1;
- 7 519 ÷ 2 = 3 759 + 1;
- 3 759 ÷ 2 = 1 879 + 1;
- 1 879 ÷ 2 = 939 + 1;
- 939 ÷ 2 = 469 + 1;
- 469 ÷ 2 = 234 + 1;
- 234 ÷ 2 = 117 + 0;
- 117 ÷ 2 = 58 + 1;
- 58 ÷ 2 = 29 + 0;
- 29 ÷ 2 = 14 + 1;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 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.
3 850 019(10) = 11 1010 1011 1111 0010 0011(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 3 850 019(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:
3 850 019(10) = 0000 0000 0011 1010 1011 1111 0010 0011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.