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;
- 107 644 ÷ 2 = 53 822 + 0;
- 53 822 ÷ 2 = 26 911 + 0;
- 26 911 ÷ 2 = 13 455 + 1;
- 13 455 ÷ 2 = 6 727 + 1;
- 6 727 ÷ 2 = 3 363 + 1;
- 3 363 ÷ 2 = 1 681 + 1;
- 1 681 ÷ 2 = 840 + 1;
- 840 ÷ 2 = 420 + 0;
- 420 ÷ 2 = 210 + 0;
- 210 ÷ 2 = 105 + 0;
- 105 ÷ 2 = 52 + 1;
- 52 ÷ 2 = 26 + 0;
- 26 ÷ 2 = 13 + 0;
- 13 ÷ 2 = 6 + 1;
- 6 ÷ 2 = 3 + 0;
- 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.
107 644(10) = 1 1010 0100 0111 1100(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 17.
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, 17,
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 107 644(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
107 644(10) = 0000 0000 0000 0001 1010 0100 0111 1100
Spaces were used to group digits: for binary, by 4, for decimal, by 3.