85 lines
2 KiB
Python
85 lines
2 KiB
Python
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from typing import List
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def getInt():
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while True:
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try:
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value = int(input("Please enter a natural number: "))
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return value
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except ValueError:
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print("Please enter a valid natural number.")
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def getBin(x: int) -> List[int]:
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return list(map(lambda x: int(x), bin(abs(x))[2:]))
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def twosComplementToInt(bits: List[int]) -> int:
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sum = 0 if bits[0] == 0 else -(2 ** (len(bits) - 1))
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del bits[0]
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bits.reverse()
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for i in range(len(bits)):
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if bits[i] == 1:
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sum += 2 ** i
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return sum
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def add(x: int, y: int) -> int:
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bits = max(len(bin(x)[2:]), len(bin(y)[2:])) + 1
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mask = int("1" * bits, 2)
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xBin = list(map(lambda x: int(x), ("0" if x >= 0 else "1") + bin(x & mask)[2:]))
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yBin = list(map(lambda x: int(x), ("0" if y >= 0 else "1") + bin(y & mask)[2:]))
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print(xBin, yBin)
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# Pad the shortner binary number
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while len(xBin) < bits:
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xBin.insert(0, 0)
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while len(yBin) < bits:
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yBin.insert(0, 0)
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# We add from right to left
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xBin.reverse(); yBin.reverse()
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# Iteratively apply the full adder
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cout = 0
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outBin = []
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for a, b in zip(xBin, yBin):
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sum = cout ^ (a ^ b)
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cout = (a & b) | (cout & ((~a & b) | (a & ~b)))
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outBin.append(sum)
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if x > 0 and y > 0: outBin.append(cout)
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# We read from left to right
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outBin.reverse()
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print(outBin)
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return twosComplementToInt(outBin)
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def subtract(x: int, y: int) -> int:
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return add(x, -y)
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def multiply(x: int, y: int) -> int:
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if x == 1:
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return y
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elif x == -1:
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return -y
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elif y == 1:
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return x
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elif y == -1:
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return -x
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sgn = -1 if (x > 0 and y < 0) or (y > 0 and x < 0) else 1
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product = 0
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for num in [abs(x) for _ in range(abs(y))]:
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product = add(product, num)
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return multiply(sgn, product)
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x, y = getInt(), getInt()
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# Compare the results
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print(x + y, add(x, y))
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