Find 2's complement 00010110
Answers
Answer:
0001 0110(2) = 22(10)
Explanation:
1. Is this a positive or a negative number?
In a signed binary two's complement, first bit (the leftmost) indicates the sign,
1 = negative, 0 = positive.
0001 0110 is the binary representation of a positive integer, on 8 bits.
2. Get the binary representation in one's complement:
* Run this step only if the number is negative *
Subtract 1 from the binary initial number:
* Not the case *
2. Get the binary representation of the positive (unsigned) number:
* Run this step only if the number is negative *
Flip all the bits in the signed binary one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
* Not the case *
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
27
0
26
0
25
0
24
1
23
0
22
1
21
1
20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up:
0001 0110(2) =
(0 × 27 + 0 × 26 + 0 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 0 × 20)(10) =
(0 + 0 + 0 + 16 + 0 + 4 + 2 + 0)(10) =
(16 + 4 + 2)(10) =
22(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0001 0110(2) = 22(10)