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;
- 11 101 170 ÷ 2 = 5 550 585 + 0;
- 5 550 585 ÷ 2 = 2 775 292 + 1;
- 2 775 292 ÷ 2 = 1 387 646 + 0;
- 1 387 646 ÷ 2 = 693 823 + 0;
- 693 823 ÷ 2 = 346 911 + 1;
- 346 911 ÷ 2 = 173 455 + 1;
- 173 455 ÷ 2 = 86 727 + 1;
- 86 727 ÷ 2 = 43 363 + 1;
- 43 363 ÷ 2 = 21 681 + 1;
- 21 681 ÷ 2 = 10 840 + 1;
- 10 840 ÷ 2 = 5 420 + 0;
- 5 420 ÷ 2 = 2 710 + 0;
- 2 710 ÷ 2 = 1 355 + 0;
- 1 355 ÷ 2 = 677 + 1;
- 677 ÷ 2 = 338 + 1;
- 338 ÷ 2 = 169 + 0;
- 169 ÷ 2 = 84 + 1;
- 84 ÷ 2 = 42 + 0;
- 42 ÷ 2 = 21 + 0;
- 21 ÷ 2 = 10 + 1;
- 10 ÷ 2 = 5 + 0;
- 5 ÷ 2 = 2 + 1;
- 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.
11 101 170(10) = 1010 1001 0110 0011 1111 0010(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 24.
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, 24,
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.
11 101 170(10) = 0000 0000 1010 1001 0110 0011 1111 0010
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.
-11 101 170(10) = !(0000 0000 1010 1001 0110 0011 1111 0010)
Number -11 101 170(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:
-11 101 170(10) = 1111 1111 0101 0110 1001 1100 0000 1101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.