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;
- 2 147 516 416 ÷ 2 = 1 073 758 208 + 0;
- 1 073 758 208 ÷ 2 = 536 879 104 + 0;
- 536 879 104 ÷ 2 = 268 439 552 + 0;
- 268 439 552 ÷ 2 = 134 219 776 + 0;
- 134 219 776 ÷ 2 = 67 109 888 + 0;
- 67 109 888 ÷ 2 = 33 554 944 + 0;
- 33 554 944 ÷ 2 = 16 777 472 + 0;
- 16 777 472 ÷ 2 = 8 388 736 + 0;
- 8 388 736 ÷ 2 = 4 194 368 + 0;
- 4 194 368 ÷ 2 = 2 097 184 + 0;
- 2 097 184 ÷ 2 = 1 048 592 + 0;
- 1 048 592 ÷ 2 = 524 296 + 0;
- 524 296 ÷ 2 = 262 148 + 0;
- 262 148 ÷ 2 = 131 074 + 0;
- 131 074 ÷ 2 = 65 537 + 0;
- 65 537 ÷ 2 = 32 768 + 1;
- 32 768 ÷ 2 = 16 384 + 0;
- 16 384 ÷ 2 = 8 192 + 0;
- 8 192 ÷ 2 = 4 096 + 0;
- 4 096 ÷ 2 = 2 048 + 0;
- 2 048 ÷ 2 = 1 024 + 0;
- 1 024 ÷ 2 = 512 + 0;
- 512 ÷ 2 = 256 + 0;
- 256 ÷ 2 = 128 + 0;
- 128 ÷ 2 = 64 + 0;
- 64 ÷ 2 = 32 + 0;
- 32 ÷ 2 = 16 + 0;
- 16 ÷ 2 = 8 + 0;
- 8 ÷ 2 = 4 + 0;
- 4 ÷ 2 = 2 + 0;
- 2 ÷ 2 = 1 + 0;
- 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.
2 147 516 416(10) = 1000 0000 0000 0000 1000 0000 0000 0000(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 32.
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, 32,
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 2 147 516 416(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
2 147 516 416(10) = 0000 0000 0000 0000 0000 0000 0000 0000 1000 0000 0000 0000 1000 0000 0000 0000
Spaces were used to group digits: for binary, by 4, for decimal, by 3.