Write 2 functions using iterations:
* while loop: While loops are iterating if statements – while a condition is true keep looping* for loop: For loops have a known start, stop and increment/decrement value to keep looping
These functions determine the binary bit-pattern of a decimal number. There are a number of bitwise operators that can be used to determine the bit-pattern. See Bitwise.py for examples of using bitwise operators. Here’s a general algorithm that can be used (that doesn’t use looping):
Algorithm Bitpattern(number)1 if number & (1 << 0) > 0 # check first bit2 print(1)3 else4 print(0)5 if number & (1 << 1) > 0 # check second bit6 print(1)7 else8 print(0) 9 if number & (1 << 2) > 0 # check third bit10 print(1)11 else12 print(0) 13 “¦ etc.
The problem will be when to stop shifting while looping. A way to determine the number of shifts can be found using logarithms:
Algorithm ShiftBits(number) log10 = math.log(number+1) log2 = log10 / math.log(2) shifts = math.ceil(log2) return shifts
Note: To use the log or ceil function:
1. First: import math 2. To call the ceil or log function: math.log(number) or math.ceil(number)
Consequently, to determine the number of iterations for a FOR loop using decimal 10 is 4. Here’s proof:
2**0 = 12**1 = 22**2 = 42**3 = 8
Decimal(10) = 1(2**3[8]) + 0(2**2[4]) + 1(2**1[2]) + 0(2**0)[1]) = 1010 binary