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;
- 157 239 807 ÷ 2 = 78 619 903 + 1;
- 78 619 903 ÷ 2 = 39 309 951 + 1;
- 39 309 951 ÷ 2 = 19 654 975 + 1;
- 19 654 975 ÷ 2 = 9 827 487 + 1;
- 9 827 487 ÷ 2 = 4 913 743 + 1;
- 4 913 743 ÷ 2 = 2 456 871 + 1;
- 2 456 871 ÷ 2 = 1 228 435 + 1;
- 1 228 435 ÷ 2 = 614 217 + 1;
- 614 217 ÷ 2 = 307 108 + 1;
- 307 108 ÷ 2 = 153 554 + 0;
- 153 554 ÷ 2 = 76 777 + 0;
- 76 777 ÷ 2 = 38 388 + 1;
- 38 388 ÷ 2 = 19 194 + 0;
- 19 194 ÷ 2 = 9 597 + 0;
- 9 597 ÷ 2 = 4 798 + 1;
- 4 798 ÷ 2 = 2 399 + 0;
- 2 399 ÷ 2 = 1 199 + 1;
- 1 199 ÷ 2 = 599 + 1;
- 599 ÷ 2 = 299 + 1;
- 299 ÷ 2 = 149 + 1;
- 149 ÷ 2 = 74 + 1;
- 74 ÷ 2 = 37 + 0;
- 37 ÷ 2 = 18 + 1;
- 18 ÷ 2 = 9 + 0;
- 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.
157 239 807(10) = 1001 0101 1111 0100 1001 1111 1111(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 28.
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) indicates 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, 28,
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 157 239 807(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
157 239 807(10) = 0000 1001 0101 1111 0100 1001 1111 1111
Spaces were used to group digits: for binary, by 4, for decimal, by 3.