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;
- 16 843 257 ÷ 2 = 8 421 628 + 1;
- 8 421 628 ÷ 2 = 4 210 814 + 0;
- 4 210 814 ÷ 2 = 2 105 407 + 0;
- 2 105 407 ÷ 2 = 1 052 703 + 1;
- 1 052 703 ÷ 2 = 526 351 + 1;
- 526 351 ÷ 2 = 263 175 + 1;
- 263 175 ÷ 2 = 131 587 + 1;
- 131 587 ÷ 2 = 65 793 + 1;
- 65 793 ÷ 2 = 32 896 + 1;
- 32 896 ÷ 2 = 16 448 + 0;
- 16 448 ÷ 2 = 8 224 + 0;
- 8 224 ÷ 2 = 4 112 + 0;
- 4 112 ÷ 2 = 2 056 + 0;
- 2 056 ÷ 2 = 1 028 + 0;
- 1 028 ÷ 2 = 514 + 0;
- 514 ÷ 2 = 257 + 0;
- 257 ÷ 2 = 128 + 1;
- 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;
3. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
16 843 257(10) = 1 0000 0001 0000 0001 1111 1001(2)
4. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 25.
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, 25,
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:
16 843 257(10) = 0000 0001 0000 0001 0000 0001 1111 1001
6. Get the negative integer number representation:
To get the negative integer number representation on 32 bits (4 Bytes),
... change the first bit (the leftmost), from 0 to 1...
Number -16 843 257(10), a signed integer number (with sign),
converted from decimal system (from base 10)
and written as a signed binary (in base 2):
-16 843 257(10) = 1000 0001 0000 0001 0000 0001 1111 1001
Spaces were used to group digits: for binary, by 4, for decimal, by 3.