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;
- 140 190 273 ÷ 2 = 70 095 136 + 1;
- 70 095 136 ÷ 2 = 35 047 568 + 0;
- 35 047 568 ÷ 2 = 17 523 784 + 0;
- 17 523 784 ÷ 2 = 8 761 892 + 0;
- 8 761 892 ÷ 2 = 4 380 946 + 0;
- 4 380 946 ÷ 2 = 2 190 473 + 0;
- 2 190 473 ÷ 2 = 1 095 236 + 1;
- 1 095 236 ÷ 2 = 547 618 + 0;
- 547 618 ÷ 2 = 273 809 + 0;
- 273 809 ÷ 2 = 136 904 + 1;
- 136 904 ÷ 2 = 68 452 + 0;
- 68 452 ÷ 2 = 34 226 + 0;
- 34 226 ÷ 2 = 17 113 + 0;
- 17 113 ÷ 2 = 8 556 + 1;
- 8 556 ÷ 2 = 4 278 + 0;
- 4 278 ÷ 2 = 2 139 + 0;
- 2 139 ÷ 2 = 1 069 + 1;
- 1 069 ÷ 2 = 534 + 1;
- 534 ÷ 2 = 267 + 0;
- 267 ÷ 2 = 133 + 1;
- 133 ÷ 2 = 66 + 1;
- 66 ÷ 2 = 33 + 0;
- 33 ÷ 2 = 16 + 1;
- 16 ÷ 2 = 8 + 0;
- 8 ÷ 2 = 4 + 0;
- 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.
140 190 273(10) = 1000 0101 1011 0010 0010 0100 0001(2)
4. 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) 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, 28,
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:
140 190 273(10) = 0000 1000 0101 1011 0010 0010 0100 0001
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 -140 190 273(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-140 190 273(10) = 1000 1000 0101 1011 0010 0010 0100 0001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.