2. 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;
- 1 910 538 234 ÷ 2 = 955 269 117 + 0;
- 955 269 117 ÷ 2 = 477 634 558 + 1;
- 477 634 558 ÷ 2 = 238 817 279 + 0;
- 238 817 279 ÷ 2 = 119 408 639 + 1;
- 119 408 639 ÷ 2 = 59 704 319 + 1;
- 59 704 319 ÷ 2 = 29 852 159 + 1;
- 29 852 159 ÷ 2 = 14 926 079 + 1;
- 14 926 079 ÷ 2 = 7 463 039 + 1;
- 7 463 039 ÷ 2 = 3 731 519 + 1;
- 3 731 519 ÷ 2 = 1 865 759 + 1;
- 1 865 759 ÷ 2 = 932 879 + 1;
- 932 879 ÷ 2 = 466 439 + 1;
- 466 439 ÷ 2 = 233 219 + 1;
- 233 219 ÷ 2 = 116 609 + 1;
- 116 609 ÷ 2 = 58 304 + 1;
- 58 304 ÷ 2 = 29 152 + 0;
- 29 152 ÷ 2 = 14 576 + 0;
- 14 576 ÷ 2 = 7 288 + 0;
- 7 288 ÷ 2 = 3 644 + 0;
- 3 644 ÷ 2 = 1 822 + 0;
- 1 822 ÷ 2 = 911 + 0;
- 911 ÷ 2 = 455 + 1;
- 455 ÷ 2 = 227 + 1;
- 227 ÷ 2 = 113 + 1;
- 113 ÷ 2 = 56 + 1;
- 56 ÷ 2 = 28 + 0;
- 28 ÷ 2 = 14 + 0;
- 14 ÷ 2 = 7 + 0;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 1 ÷ 2 = 0 + 1;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
1 910 538 234(10) = 111 0001 1110 0000 0111 1111 1111 1010(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 31.
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, 31,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
5. 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:
1 910 538 234(10) = 0111 0001 1110 0000 0111 1111 1111 1010
6. Get the negative integer number representation:
To get the negative integer number representation on 32 bits (4 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -1 910 538 234(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-1 910 538 234(10) = 1111 0001 1110 0000 0111 1111 1111 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.