A very busy week, so today’s post is just a code snippet which converts a decimal number to bits.  Notice that you can go inside the code and adjust how many bits are given to exponents and to the mantissa.  I’ve adjusted a bit to try to help the formatting, but I want to prioritize copying and pasting.  Let me know any problems/criticisms of the code!

from math import log,floor

def bitrep(mbits,ebits):
	#this function writes a float N = sign*M*2**(E-offset), where sign = 0 or 
	#1, M ranges from 2**0 up to 2**(mbits+1)-1 and E ranges from 2**0 up to 
	#2**(ebits+1)-1.  The numbers sign,M,N are then converted to binary, and 
	#sign,M,N are then returned.  To get the bit representation of a double, 
	#set mbits = 52, ebits = 11.
	mbits +=1
	offset = 2**(ebits-1)-1
	N = input('What decimal do you want the bit representation of?\n> ')

	#find the sign of the number
	if N >= 0:
		S = '0'
	else:
		S = '1'

	N = abs(N)
	#find the size of the number's exponent
	E= int(floor(log(N,2)))+offset-mbits

	#convert N into the fraction n/d, where d is a power of 10.
	n = str(N)
	try:
		d = 10**(len(n)-n.index('.')-1)
		n = int(d*N)
	except(ValueError):
		try:
			d = 10**(len(n)-n.index('e')-1)
			n = int(d*N)
		except(ValueError):
			d = 1
			n = N

	#finds the mantissa of N
	if offset>=E:
		if d == 1:
			M = N*2**(-E+offset)
		else:
			M,r = divmod(n*2**(-E+offset),d)
			if r>=d/2:
				M+=1
	else:
		M,r = divmod(N,2**(E-offset))
		if r >= (E-offset)/2:
			M+=1

	#converts both the exponent and mantissa to binary
	Ebin = bin(E-1)
	Ebin = Ebin[Ebin.index('b')+1:]
	Mbin = bin(M)[3:]

	#pads each number up to the total number of bits
	Ebin = Ebin.zfill(ebits)
	Mbin = Mbin.zfill(mbits)
	#cuts the mantissa back down to mbits of length, if necessary
	Mbin = Mbin[:mbits-1]

	#print out with the mantissa and exponent, then carrying out the 
	#calculation with python, then in bits
	print N,'\t"="',M,'* (2**[',E,'-',offset,'])\n','\t = ',M*(2**(E-offset)),'\n',S,Ebin,Mbin

bitrep(52,11)

I think the default Mac terminal colors are different from this, but you can change them in "preferences"

This is intended as a quick guide, since one of the things that got me into programming was realizing how quickly I could start on my Apple laptop without installing anything.  As a practice first project, we’ll first compute the first 10 Fibonacci numbers, then write a function that will do this.
1. Finding Python.  The easiest way to get started is to just hit “cmd+space” (this opens spotlight: my favorite Mac feature), then type “terminal”, and open the terminal.  After that, it is as easy as typing python, and you have either a powerful calculator, or a way to start writing scripts.
2. Fibonacci. As a nice first calculation, we’ll save two variables to initialize the Fibonacci sequence, then run a loop 99 times (I had to play around a bit to see how the loop count corresponded to where in the Fibonacci sequence I was). See the image for this section.  Note that the spaces are very important.  You need to end lines with a colon, and start lines after the colon by indenting.  See below for more proper indenting.

Wikipedia claims the first Fibonacci number is 0, which I am ignoring for this post.

3. Function. Now to write a helper function that I can use to calculate many such numbers, I will open a text file (just in TextEdit), type in the code below, and save it as Fib.py:

def Fib(n):
#calculate the nth digit of the Fibonacci sequence
a,b = 1,0
for j in range(n):
a,b = a+b,a
return a

for j in range(10):
print Fib(j)

You can also see this post in progress behind the semi-opaque terminal!

4. Running a script. Now go back to the terminal window, hit “ctrl+d” to get out of Python, and navigate to the folder where you saved Fib.py. Mine was in “colcarroll/mystuff/blog”. Once there, just type “python Fib.py“, and the terminal will print out anything you asked to be printed out. Above, I print out the first 10 Fibonacci numbers.

Cheers! Now go find a proper introduction. Or use Project Euler.