I'm currently working on the last project in Nand2Tetris course.
I've been trying to figure out how the logic expression works while implementing a bit-wise calculation.
How Python can catch the right digits of 16-bit binary that correspond to an integer y when the twoToThe[i] == 0 (5 is 101 in binary, thus twoToThe[0] == 0 and twoToThe[2] == 0 are False and it's the right answer)
but why does not show the exact opposite result when twoToThe[i] == 1?
I thought it would return True on both twoTwoThe[0] == 1 and twoTwoThe[2] == 1
Here's code below
# Calculating x * y
x = 3 # doesn't matter here
y = 5
# Array that holds i'th bit's integer values in 16-bit binary (e.g. twoToThe[4] = 16)
twoToThe = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768]
## Set twoToThe[i] == 0
print(y & twoToThe[0] == 0) # False (101 is 5, so False is right)
print(y & twoToThe[1] == 0) # True
print(y & twoToThe[2] == 0) # False (101 is 5, so False is right)
print(y & twoToThe[3] == 0) # True
print(y & twoToThe[4] == 0) # True
print(y & twoToThe[5] == 0) # True
...
print(y & twoToThe[15] == 1) # False
## Set twoToThe[i] == 1
print(y & twoToThe[0] == 1) # True
print(y & twoToThe[1] == 1) # False
print(y & twoToThe[2] == 1) # False (I expected True here, but it's false)
print(y & twoToThe[3] == 1) # False
print(y & twoToThe[4] == 1) # False
print(y & twoToThe[5] == 1) # False
...
print(y & twoToThe[15] == 1) # False
The y & twoToThe[0] expressions evaluates to a new integer (as a result of a bitwise and operation between the bits of 5 and the bits of twoToThe[i]), not to a boolean as I think you were expecting. Check it:
y = 5
# Array that holds i'th bit's integer values in 16-bit binary (e.g. twoToThe[4] = 16)
twoToThe = [1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768]
print(type(y & twoToThe[0])) #int
print(y & twoToThe[0]) # 1
print(y & twoToThe[1]) # 0
print(y & twoToThe[2]) # 4
print(y & twoToThe[3]) # 0
print(y & twoToThe[4]) # 0
print(y & twoToThe[5]) # 0