bitwise operation and Two's complement in python

Question

I have an array of (short) data which is shifted 4 to left and it is also a signed number. I need to plot it around zero.

for instance: if the number in the array is 0b0000000011111111 and I shift it to left by 4, I will get 0b000000001111. it is fine.

for instance: if the number in the array is 0b100011111111 and I shift it to left by 4, I will get 0b000010001111. It is fine, but now it is not a negative number.

can someone help ?

Your question is not clear. In both instances, you say "shift it to left" but it looks like a shift to the *right* (toward the least significant bit). Do you mean "shift it to the right"? Also, the problem itself is not clear. Do you want to shift negative numbers and still get a negative number? Also, just how do you do the shifts? What is the data format of the numbers--16 bit integers? What kind of variable is it in? — Rory Daulton, Aug 08 '18 at 07:24
The only solution I can think of is to convert them to positive numbers before making the shift and then back to negative. [This wikipedia page](https://en.wikipedia.org/wiki/Two's_complement) provides a good explanation of how two's compliment works. — Bill, Aug 08 '18 at 07:25
Python doesn't use two's complement in its integers, `0b10001111111 == 2303`. — jonrsharpe, Aug 08 '18 at 07:25
@ jonrsharpe FYI you're missing a `1` at the end (`0b100011111111`). — Bill, Aug 08 '18 at 07:28

score 1 · Accepted Answer · answered Aug 08 '18 at 08:32

You have to write your own implementation of the arithmetic right shift of a 16-bit value, if this is what you need. I suggest you this one, very easy to understand:

def arithmetic_right_shift_on_16_bits(val, n):
    # Get the sign bit
    s = val & 0x8000
    # Perform the shifts, padding with the sign bit
    for _ in range(n):
        val >>= 1
        val |= s
    return val

a = arithmetic_right_shift_on_16_bits(0b0000000011111111, 4)
print(bin(a)) # 0b1111

b = arithmetic_right_shift_on_16_bits(0b1000000011111111, 4)
print(bin(b)) # 0b1111100000001111

score 0 · Answer 2 · answered Aug 08 '18 at 07:33

0

This does not happen in Python:

>>> bin(0b0000000011111111 >> 4)  # 15
'0b1111'
>>> bin(0b100011111111 >> 4)  # 143
'0b10001111'

answered Aug 08 '18 at 07:33

L3viathan

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score 0 · Answer 3 · answered Aug 08 '18 at 08:00

BTW, the number you show as an example of a negative short integer is not one, because you gave only 12 bits. So I will assume that the number of interest is 0b1000000011111111. As Python does not use 2's complement, it is shown as 33023. But you can do the 2's complement by hand: for a short int (16 bits), you just substract 0x10000 to the number.

You can then write:

def short_signed_right_shift(x, i):
    if x < 0 or x >= 0x10000: raise ValueError   # only accept 16 bits numbers
    return x >> i if (x < 0x7FFF) else 0x10000 + ((x - 0x10000) >> i)

You can then use it:

>>> bin(short_signed_right_shift(0b0000000011111111, 4))
'0b1111'
>>> bin(short_signed_right_shift(0b1000000011111111, 4))
'0b1111100000001111'

bitwise operation and Two's complement in python

3 Answers3