One's Complement: Integer -> Binary: 11 Convert the Integer Number to a Signed Binary in One's Complement Representation. Write the Base Ten Decimal System Number as a Binary Code (Written in Base Two)
Signed integer number 11(10) converted and written as a signed binary in one's complement representation (base 2) = ?
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;
- 11 ÷ 2 = 5 + 1;
- 5 ÷ 2 = 2 + 1;
- 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.
11(10) = 1011(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 4.
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, 4,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 8.
4. Get the positive binary computer representation on 8 bits:
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 8.
Number 11(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:
11(10) = 0000 1011
Spaces were used to group digits: for binary, by 4, for decimal, by 3.
Convert signed integer numbers from the decimal system (base ten) to signed binary in one's complement representation
How to convert a base 10 signed integer number to signed binary in one's complement representation:
1) Divide the positive version of the number repeatedly by 2, keeping track of each remainder, till getting a quotient that is 0.
2) Construct the base 2 representation by taking the previously calculated remainders starting from the last remainder up to the first one, in that order.
3) Construct the positive binary computer representation so that the first bit is 0.
4) Only if the initial number is negative, switch all the bits from 0 to 1 and from 1 to 0 (reversing the digits).