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;
- 2 097 074 ÷ 2 = 1 048 537 + 0;
- 1 048 537 ÷ 2 = 524 268 + 1;
- 524 268 ÷ 2 = 262 134 + 0;
- 262 134 ÷ 2 = 131 067 + 0;
- 131 067 ÷ 2 = 65 533 + 1;
- 65 533 ÷ 2 = 32 766 + 1;
- 32 766 ÷ 2 = 16 383 + 0;
- 16 383 ÷ 2 = 8 191 + 1;
- 8 191 ÷ 2 = 4 095 + 1;
- 4 095 ÷ 2 = 2 047 + 1;
- 2 047 ÷ 2 = 1 023 + 1;
- 1 023 ÷ 2 = 511 + 1;
- 511 ÷ 2 = 255 + 1;
- 255 ÷ 2 = 127 + 1;
- 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.
2 097 074(10) = 1 1111 1111 1111 1011 0010(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 21.
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, 21,
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 2 097 074(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:
2 097 074(10) = 0000 0000 0001 1111 1111 1111 1011 0010
Spaces were used to group digits: for binary, by 4, for decimal, by 3.