........ Machine Data A computer is a machine (some built with current, oil, even steam!) that stores only

bits of information ('1’s and '0’s), and this is the language of the machine. We group

together bits of data (to form Bytes, Kilo-Bytes, Giga-Bytes, etc.) to store more

complex data. As an example, consider a light switch. It does a good job of turning

on and off lights, but what if we wanted three settings: on, dim, and off? For this, we

would need a special type of switch that could represent these three options? For

hardware reasons (cost, primarily), we can store a bit efficiently and cheaply. To

represent the three states of the lights above (on, dim, off), we would just chain two

bits together and assign 00 to be “off”, 01 to be “dim” and 10 to be “on". Notice that

we have one left over, unused binary combination here: 11. If we want to store

anything more than the number 2, or anything more than an on/off or true/false

value, we use this combination technique to combine simple data items into more

complex data items. Google and define the term Machine Language. 2. If a true/false value can be represented with one bit, and a three-setting

lighting ﬁxture can be represented with just two bits, so how many positive

integers can be represented with just 3 bits? a. Hint: Binary is base 2, so consider 2 raised to the power of 3 3. If our alphabet contains 26 distinct letters, how many bits do we need to

represent a single letter? b. Hint: The inverse of the power function is the logarithm, so consider

X, where X = logz 26. Rewrite this as 2’1 = 26, and determine X.

Further hint: Since you can’t have fractions of a bit, you need to use

the ceiling function to raise your X value to a whole number. CS SPOILER ALERT! [STORED PROGRAM CONCEPT] You store numbers (data) in binary. You also store software (methods) in binary.

This is the stored program concept, and it means we can use binary RAM to store

results from a football tournament (data), or we could use the same binary RAM to

store a program that calculates the winner of the football tournament, using the

same tool: a bit (a.k.a RAM, FIipFl'op, Latch, SR Latch, Memory). It means that if

you look at any arbitrary chunk of RAM, it could ho ld data or a pro gram, and you

wouldn’t necessarily know which just by looking at the bits.