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;
- 1 247 092 986 ÷ 2 = 623 546 493 + 0;
- 623 546 493 ÷ 2 = 311 773 246 + 1;
- 311 773 246 ÷ 2 = 155 886 623 + 0;
- 155 886 623 ÷ 2 = 77 943 311 + 1;
- 77 943 311 ÷ 2 = 38 971 655 + 1;
- 38 971 655 ÷ 2 = 19 485 827 + 1;
- 19 485 827 ÷ 2 = 9 742 913 + 1;
- 9 742 913 ÷ 2 = 4 871 456 + 1;
- 4 871 456 ÷ 2 = 2 435 728 + 0;
- 2 435 728 ÷ 2 = 1 217 864 + 0;
- 1 217 864 ÷ 2 = 608 932 + 0;
- 608 932 ÷ 2 = 304 466 + 0;
- 304 466 ÷ 2 = 152 233 + 0;
- 152 233 ÷ 2 = 76 116 + 1;
- 76 116 ÷ 2 = 38 058 + 0;
- 38 058 ÷ 2 = 19 029 + 0;
- 19 029 ÷ 2 = 9 514 + 1;
- 9 514 ÷ 2 = 4 757 + 0;
- 4 757 ÷ 2 = 2 378 + 1;
- 2 378 ÷ 2 = 1 189 + 0;
- 1 189 ÷ 2 = 594 + 1;
- 594 ÷ 2 = 297 + 0;
- 297 ÷ 2 = 148 + 1;
- 148 ÷ 2 = 74 + 0;
- 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;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
1 247 092 986(10) = 100 1010 0101 0101 0010 0000 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) 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, 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.
1 247 092 986(10) = 0100 1010 0101 0101 0010 0000 1111 1010
6. Get the negative integer number representation:
To write the negative integer number on 32 bits (4 Bytes),
as a signed binary in one's complement representation,
... replace all the bits on 0 with 1s and all the bits set on 1 with 0s.
Reverse the digits, flip the digits:
Replace the bits set on 0 with 1s and the bits set on 1 with 0s.
-1 247 092 986(10) = !(0100 1010 0101 0101 0010 0000 1111 1010)
Number -1 247 092 986(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:
-1 247 092 986(10) = 1011 0101 1010 1010 1101 1111 0000 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.