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;
- 19 127 337 ÷ 2 = 9 563 668 + 1;
- 9 563 668 ÷ 2 = 4 781 834 + 0;
- 4 781 834 ÷ 2 = 2 390 917 + 0;
- 2 390 917 ÷ 2 = 1 195 458 + 1;
- 1 195 458 ÷ 2 = 597 729 + 0;
- 597 729 ÷ 2 = 298 864 + 1;
- 298 864 ÷ 2 = 149 432 + 0;
- 149 432 ÷ 2 = 74 716 + 0;
- 74 716 ÷ 2 = 37 358 + 0;
- 37 358 ÷ 2 = 18 679 + 0;
- 18 679 ÷ 2 = 9 339 + 1;
- 9 339 ÷ 2 = 4 669 + 1;
- 4 669 ÷ 2 = 2 334 + 1;
- 2 334 ÷ 2 = 1 167 + 0;
- 1 167 ÷ 2 = 583 + 1;
- 583 ÷ 2 = 291 + 1;
- 291 ÷ 2 = 145 + 1;
- 145 ÷ 2 = 72 + 1;
- 72 ÷ 2 = 36 + 0;
- 36 ÷ 2 = 18 + 0;
- 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.
19 127 337(10) = 1 0010 0011 1101 1100 0010 1001(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 25.
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, 25,
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 19 127 337(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
19 127 337(10) = 0000 0001 0010 0011 1101 1100 0010 1001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.