1. 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;
- 266 438 546 ÷ 2 = 133 219 273 + 0;
- 133 219 273 ÷ 2 = 66 609 636 + 1;
- 66 609 636 ÷ 2 = 33 304 818 + 0;
- 33 304 818 ÷ 2 = 16 652 409 + 0;
- 16 652 409 ÷ 2 = 8 326 204 + 1;
- 8 326 204 ÷ 2 = 4 163 102 + 0;
- 4 163 102 ÷ 2 = 2 081 551 + 0;
- 2 081 551 ÷ 2 = 1 040 775 + 1;
- 1 040 775 ÷ 2 = 520 387 + 1;
- 520 387 ÷ 2 = 260 193 + 1;
- 260 193 ÷ 2 = 130 096 + 1;
- 130 096 ÷ 2 = 65 048 + 0;
- 65 048 ÷ 2 = 32 524 + 0;
- 32 524 ÷ 2 = 16 262 + 0;
- 16 262 ÷ 2 = 8 131 + 0;
- 8 131 ÷ 2 = 4 065 + 1;
- 4 065 ÷ 2 = 2 032 + 1;
- 2 032 ÷ 2 = 1 016 + 0;
- 1 016 ÷ 2 = 508 + 0;
- 508 ÷ 2 = 254 + 0;
- 254 ÷ 2 = 127 + 0;
- 127 ÷ 2 = 63 + 1;
- 63 ÷ 2 = 31 + 1;
- 31 ÷ 2 = 15 + 1;
- 15 ÷ 2 = 7 + 1;
- 7 ÷ 2 = 3 + 1;
- 3 ÷ 2 = 1 + 1;
- 1 ÷ 2 = 0 + 1;
2. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
266 438 546(10) = 1111 1110 0001 1000 0111 1001 0010(2)
3. 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) 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, 28,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 32.
4. 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.
Number 266 438 546(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in two's complement representation:
266 438 546(10) = 0000 1111 1110 0001 1000 0111 1001 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.