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;
- 10 010 101 ÷ 2 = 5 005 050 + 1;
- 5 005 050 ÷ 2 = 2 502 525 + 0;
- 2 502 525 ÷ 2 = 1 251 262 + 1;
- 1 251 262 ÷ 2 = 625 631 + 0;
- 625 631 ÷ 2 = 312 815 + 1;
- 312 815 ÷ 2 = 156 407 + 1;
- 156 407 ÷ 2 = 78 203 + 1;
- 78 203 ÷ 2 = 39 101 + 1;
- 39 101 ÷ 2 = 19 550 + 1;
- 19 550 ÷ 2 = 9 775 + 0;
- 9 775 ÷ 2 = 4 887 + 1;
- 4 887 ÷ 2 = 2 443 + 1;
- 2 443 ÷ 2 = 1 221 + 1;
- 1 221 ÷ 2 = 610 + 1;
- 610 ÷ 2 = 305 + 0;
- 305 ÷ 2 = 152 + 1;
- 152 ÷ 2 = 76 + 0;
- 76 ÷ 2 = 38 + 0;
- 38 ÷ 2 = 19 + 0;
- 19 ÷ 2 = 9 + 1;
- 9 ÷ 2 = 4 + 1;
- 4 ÷ 2 = 2 + 0;
- 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.
10 010 101(10) = 1001 1000 1011 1101 1111 0101(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 24.
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, 24,
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 10 010 101(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
10 010 101(10) = 0000 0000 1001 1000 1011 1101 1111 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.