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;
- 55 975 525 ÷ 2 = 27 987 762 + 1;
- 27 987 762 ÷ 2 = 13 993 881 + 0;
- 13 993 881 ÷ 2 = 6 996 940 + 1;
- 6 996 940 ÷ 2 = 3 498 470 + 0;
- 3 498 470 ÷ 2 = 1 749 235 + 0;
- 1 749 235 ÷ 2 = 874 617 + 1;
- 874 617 ÷ 2 = 437 308 + 1;
- 437 308 ÷ 2 = 218 654 + 0;
- 218 654 ÷ 2 = 109 327 + 0;
- 109 327 ÷ 2 = 54 663 + 1;
- 54 663 ÷ 2 = 27 331 + 1;
- 27 331 ÷ 2 = 13 665 + 1;
- 13 665 ÷ 2 = 6 832 + 1;
- 6 832 ÷ 2 = 3 416 + 0;
- 3 416 ÷ 2 = 1 708 + 0;
- 1 708 ÷ 2 = 854 + 0;
- 854 ÷ 2 = 427 + 0;
- 427 ÷ 2 = 213 + 1;
- 213 ÷ 2 = 106 + 1;
- 106 ÷ 2 = 53 + 0;
- 53 ÷ 2 = 26 + 1;
- 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.
55 975 525(10) = 11 0101 0110 0001 1110 0110 0101(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 55 975 525(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
55 975 525(10) = 0000 0011 0101 0110 0001 1110 0110 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.