Bitwise not, can somebody explain this example?

Question

Can somebody explain this example through binary digits?

>>> ~11
-12

https://en.wikipedia.org/wiki/Two%27s_complement – VPfB Dec 15 '17 at 19:45 — VPfB, Dec 15 '17 at 19:45
See also: https://stackoverflow.com/a/31151236/8881141 – Mr. T Dec 15 '17 at 20:00 — Mr. T, Dec 15 '17 at 20:00

score 1 · Accepted Answer · answered Dec 15 '17 at 19:58

1

Using 8 bit representation (you can use larger representations for the same results):

~11 => ~ b 00001011

Applying NOT operator yields (1 turns to 0 and vice versa):

~(b 00001011) => b 11110100

The result is negative (since the left most bit is the sign bit). To discover its value, apply 2's complement operator (see here):

b 11110100, negate bits:
b 00001011, add 1:
+        1
----------
b 00001100 => 12

Meaning that the result was -12.

answered Dec 15 '17 at 19:58

Yaniv Shaked

698
6
12

May I asked, why -1? I believe the explanation is totally correct, will be happy to discuss if anyone thinks otherwise – Yaniv Shaked Dec 15 '17 at 20:20

score 0 · Answer 2 · answered Dec 15 '17 at 19:54

def toBinary(n):
    return ''.join(str(1 & int(n) >> i) for i in range(64)[::-1])

toBinary(11) Returns

0000000000000000000000000000000000000000000000000000000000001011

toBinary(-12) Returns

1111111111111111111111111111111111111111111111111111111111110100

From Python Docs ~x : Returns the complement of x - the number you get by switching each 1 for a 0 and each 0 for a 1. This is the same as -x - 1. For More : https://wiki.python.org/moin/BitwiseOperators

Bitwise not, can somebody explain this example?

2 Answers2