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;
- 435 345 562 ÷ 2 = 217 672 781 + 0;
- 217 672 781 ÷ 2 = 108 836 390 + 1;
- 108 836 390 ÷ 2 = 54 418 195 + 0;
- 54 418 195 ÷ 2 = 27 209 097 + 1;
- 27 209 097 ÷ 2 = 13 604 548 + 1;
- 13 604 548 ÷ 2 = 6 802 274 + 0;
- 6 802 274 ÷ 2 = 3 401 137 + 0;
- 3 401 137 ÷ 2 = 1 700 568 + 1;
- 1 700 568 ÷ 2 = 850 284 + 0;
- 850 284 ÷ 2 = 425 142 + 0;
- 425 142 ÷ 2 = 212 571 + 0;
- 212 571 ÷ 2 = 106 285 + 1;
- 106 285 ÷ 2 = 53 142 + 1;
- 53 142 ÷ 2 = 26 571 + 0;
- 26 571 ÷ 2 = 13 285 + 1;
- 13 285 ÷ 2 = 6 642 + 1;
- 6 642 ÷ 2 = 3 321 + 0;
- 3 321 ÷ 2 = 1 660 + 1;
- 1 660 ÷ 2 = 830 + 0;
- 830 ÷ 2 = 415 + 0;
- 415 ÷ 2 = 207 + 1;
- 207 ÷ 2 = 103 + 1;
- 103 ÷ 2 = 51 + 1;
- 51 ÷ 2 = 25 + 1;
- 25 ÷ 2 = 12 + 1;
- 12 ÷ 2 = 6 + 0;
- 6 ÷ 2 = 3 + 0;
- 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.
435 345 562(10) = 1 1001 1111 0010 1101 1000 1001 1010(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 29.
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, 29,
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.
435 345 562(10) = 0001 1001 1111 0010 1101 1000 1001 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.
-435 345 562(10) = !(0001 1001 1111 0010 1101 1000 1001 1010)
Number -435 345 562(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:
-435 345 562(10) = 1110 0110 0000 1101 0010 0111 0110 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.