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;
- 1 001 001 010 042 ÷ 2 = 500 500 505 021 + 0;
- 500 500 505 021 ÷ 2 = 250 250 252 510 + 1;
- 250 250 252 510 ÷ 2 = 125 125 126 255 + 0;
- 125 125 126 255 ÷ 2 = 62 562 563 127 + 1;
- 62 562 563 127 ÷ 2 = 31 281 281 563 + 1;
- 31 281 281 563 ÷ 2 = 15 640 640 781 + 1;
- 15 640 640 781 ÷ 2 = 7 820 320 390 + 1;
- 7 820 320 390 ÷ 2 = 3 910 160 195 + 0;
- 3 910 160 195 ÷ 2 = 1 955 080 097 + 1;
- 1 955 080 097 ÷ 2 = 977 540 048 + 1;
- 977 540 048 ÷ 2 = 488 770 024 + 0;
- 488 770 024 ÷ 2 = 244 385 012 + 0;
- 244 385 012 ÷ 2 = 122 192 506 + 0;
- 122 192 506 ÷ 2 = 61 096 253 + 0;
- 61 096 253 ÷ 2 = 30 548 126 + 1;
- 30 548 126 ÷ 2 = 15 274 063 + 0;
- 15 274 063 ÷ 2 = 7 637 031 + 1;
- 7 637 031 ÷ 2 = 3 818 515 + 1;
- 3 818 515 ÷ 2 = 1 909 257 + 1;
- 1 909 257 ÷ 2 = 954 628 + 1;
- 954 628 ÷ 2 = 477 314 + 0;
- 477 314 ÷ 2 = 238 657 + 0;
- 238 657 ÷ 2 = 119 328 + 1;
- 119 328 ÷ 2 = 59 664 + 0;
- 59 664 ÷ 2 = 29 832 + 0;
- 29 832 ÷ 2 = 14 916 + 0;
- 14 916 ÷ 2 = 7 458 + 0;
- 7 458 ÷ 2 = 3 729 + 0;
- 3 729 ÷ 2 = 1 864 + 1;
- 1 864 ÷ 2 = 932 + 0;
- 932 ÷ 2 = 466 + 0;
- 466 ÷ 2 = 233 + 0;
- 233 ÷ 2 = 116 + 1;
- 116 ÷ 2 = 58 + 0;
- 58 ÷ 2 = 29 + 0;
- 29 ÷ 2 = 14 + 1;
- 14 ÷ 2 = 7 + 0;
- 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.
1 001 001 010 042(10) = 1110 1001 0001 0000 0100 1111 0100 0011 0111 1010(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 40.
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, 40,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 64.
4. Get the positive binary computer representation on 64 bits (8 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64.
Number 1 001 001 010 042(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:
1 001 001 010 042(10) = 0000 0000 0000 0000 0000 0000 1110 1001 0001 0000 0100 1111 0100 0011 0111 1010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.