Binary multiplication

binary_multiple.py

from math import ceil, log

def shift_and_sign_extend(num_list, shift=1):
  length = 0
  #find the length
  for index, element in enumerate(numlist):
    tEl = element + '0' * (index * shift)
    tLen = len(tEl)
    numlist[index] = tEl
    if length < tLen:
      length = tLen
  #extra bits required due to N operand addition
  length += int(ceil(log(len(numlist))))
  
  #fix the sign extension
  for index, element in enumerate(numlist):
    if element[0] == "1":
      numlist[index] = "1" * (length - len(element))  + element
    else:
      numlist[index] = "0" * (length - len(element))  + element
      
  return (numlist, length)

def add_binary_string(num_list):
  length = len(num_list[0])
  
  count = 0
  out = ""
  for index in range(length):
    for line_index, line in enumerate(numlist):
      if line[-index-1] == "1":
        count += 1
    
    if count % 2 == 1:
      out = "1" + out
    else:
      out = "0" + out
    count = count >> 1
  
  return out
    
def signedBinString2Int(num, bit_length):
  if len(num) > bit_length:
    num = num[-bit_length:]
  out = 0
  if len(num) == bit_length and num[0] == "1":
    out = int(num, 2) - (2**bit_length)
  else:
    out = int(num, 2)
  return out
  
def gen_prod_string(numA, numB):
  prod_strings = []
  lenB = len(numB)
  for index, element in enumerate(numA[::-1]):
    if element == "1":
      prod_strings.append(numB)
    else:
      prod_strings.append("0" * lenB)
  return prod_strings

numlist = gen_prod_string("0010", "1101")
#numlist = ["0111", "11111", "111", "1111"]
#add_binary_string(numlist, 2)
numlist,_ = shift_and_sign_extend(numlist, 1)
out = add_binary_string(numlist)
for index, element in enumerate(numlist):
  print element, " ",  signedBinString2Int(element, len(element))
print '-' * len(numlist[0])
print out,  signedBinString2Int(out, len(out))