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;
- 87 878 742 ÷ 2 = 43 939 371 + 0;
- 43 939 371 ÷ 2 = 21 969 685 + 1;
- 21 969 685 ÷ 2 = 10 984 842 + 1;
- 10 984 842 ÷ 2 = 5 492 421 + 0;
- 5 492 421 ÷ 2 = 2 746 210 + 1;
- 2 746 210 ÷ 2 = 1 373 105 + 0;
- 1 373 105 ÷ 2 = 686 552 + 1;
- 686 552 ÷ 2 = 343 276 + 0;
- 343 276 ÷ 2 = 171 638 + 0;
- 171 638 ÷ 2 = 85 819 + 0;
- 85 819 ÷ 2 = 42 909 + 1;
- 42 909 ÷ 2 = 21 454 + 1;
- 21 454 ÷ 2 = 10 727 + 0;
- 10 727 ÷ 2 = 5 363 + 1;
- 5 363 ÷ 2 = 2 681 + 1;
- 2 681 ÷ 2 = 1 340 + 1;
- 1 340 ÷ 2 = 670 + 0;
- 670 ÷ 2 = 335 + 0;
- 335 ÷ 2 = 167 + 1;
- 167 ÷ 2 = 83 + 1;
- 83 ÷ 2 = 41 + 1;
- 41 ÷ 2 = 20 + 1;
- 20 ÷ 2 = 10 + 0;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 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.
87 878 742(10) = 101 0011 1100 1110 1100 0101 0110(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 27.
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, 27,
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 87 878 742(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
87 878 742(10) = 0000 0101 0011 1100 1110 1100 0101 0110
Spaces were used to group digits: for binary, by 4, for decimal, by 3.