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;
- 45 220 427 ÷ 2 = 22 610 213 + 1;
- 22 610 213 ÷ 2 = 11 305 106 + 1;
- 11 305 106 ÷ 2 = 5 652 553 + 0;
- 5 652 553 ÷ 2 = 2 826 276 + 1;
- 2 826 276 ÷ 2 = 1 413 138 + 0;
- 1 413 138 ÷ 2 = 706 569 + 0;
- 706 569 ÷ 2 = 353 284 + 1;
- 353 284 ÷ 2 = 176 642 + 0;
- 176 642 ÷ 2 = 88 321 + 0;
- 88 321 ÷ 2 = 44 160 + 1;
- 44 160 ÷ 2 = 22 080 + 0;
- 22 080 ÷ 2 = 11 040 + 0;
- 11 040 ÷ 2 = 5 520 + 0;
- 5 520 ÷ 2 = 2 760 + 0;
- 2 760 ÷ 2 = 1 380 + 0;
- 1 380 ÷ 2 = 690 + 0;
- 690 ÷ 2 = 345 + 0;
- 345 ÷ 2 = 172 + 1;
- 172 ÷ 2 = 86 + 0;
- 86 ÷ 2 = 43 + 0;
- 43 ÷ 2 = 21 + 1;
- 21 ÷ 2 = 10 + 1;
- 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.
45 220 427(10) = 10 1011 0010 0000 0010 0100 1011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 26.
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) is reserved for 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, 26,
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 45 220 427(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
45 220 427(10) = 0000 0010 1011 0010 0000 0010 0100 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.