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;
- 1 541 183 ÷ 2 = 770 591 + 1;
- 770 591 ÷ 2 = 385 295 + 1;
- 385 295 ÷ 2 = 192 647 + 1;
- 192 647 ÷ 2 = 96 323 + 1;
- 96 323 ÷ 2 = 48 161 + 1;
- 48 161 ÷ 2 = 24 080 + 1;
- 24 080 ÷ 2 = 12 040 + 0;
- 12 040 ÷ 2 = 6 020 + 0;
- 6 020 ÷ 2 = 3 010 + 0;
- 3 010 ÷ 2 = 1 505 + 0;
- 1 505 ÷ 2 = 752 + 1;
- 752 ÷ 2 = 376 + 0;
- 376 ÷ 2 = 188 + 0;
- 188 ÷ 2 = 94 + 0;
- 94 ÷ 2 = 47 + 0;
- 47 ÷ 2 = 23 + 1;
- 23 ÷ 2 = 11 + 1;
- 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.
1 541 183(10) = 1 0111 1000 0100 0011 1111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 21.
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, 21,
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 1 541 183(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
1 541 183(10) = 0000 0000 0001 0111 1000 0100 0011 1111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.