Midterm Review Questions (without Answers)

The midterm exam will be broken into two components:

A written (lecture-based) exam, on Monday, 8/9/2021

The written portion will require you to:

Understand number representation and numeric operations (from the first three labs)
Answer short-answer questions related to numeric operations and assembly

The review below, in addition to everything you wrote for your labs, is intended to be comprehensive. All topics which could potentially be on the exam are somehow covered by this review.

Questions

The leftmost bit of a 32-bit number is in what position?
```
31
```
Shifting an unsigned binary number N two positions to the left is equivalent to multipling N by what (in decimal)?
```
4 (each shift to the left is another multiplication by two, so 2²)
```
Shifting an unsigned binary number N four positions to the right is equivalent to performing truncating division (ignoring the remainder) by what (in decimal)?
```
16 (each shift to the right is another division by two, so 2⁴)
```
For ANY unsigned binary number, which bit must you look at in order to determine if the number is odd or even?
```
Bit 0 (the rightmost bit)
```
What is -8 in twos complement representation? Represent your solution using 8 bits.
```
8 in binary: 0000 1000
flip bits:   1111 0111
add 1:       1111 1000
1111 1000
```

What is 1 + 1 with a carry-in bit set?

  1
  1
+ 1
---
  1 with carry-out set

What is 1 + 1 without a carry-in bit set?

  0
  1
+ 1
---
  0 with carry-out set

What is 1 + 0 without a carry-in bit set?

  0
  1
+ 0
---
  1 without carry-out set

What is:

  11111101
+ 01000101

Specify if the result has a carry-out set and if the result sets the overflow bit.

1 11111010 
  11111101
+ 01000101
----------
  01000010

Carry-out set, overflow bit not set.

What is:

  10010110
- 11101010

Specify if the result has a carry-out set and if the result sets the overflow bit.

  10010110
- 11101010

...is equivalent to...

    10010110
+ (-11101010)

Original:  11101010
Flip bits: 00010101
Instead of adding 1 here, I'll set the carry-in bit for the add

0 00101111
  10010110
+ 00010101
----------
  10101100

Carry-out not set, overflow bit not set.

Consider an unknown binary number N. Using only bitwise operations and bitmasks, give an expression that will produce N, except that bit 7 is guaranteed to be one. Express any bitmasks using 2-digit hexadecimal.

We have a binary number that looks like this:
XXXX XXXX

...where X is an unknown bit.
We want to produce a binary number that looks like this:

1XXX XXXX

We'll need to use OR (|) for this, as OR can be forced to produce 1
as a result with an unknown number as with ((X | 1) = 1).
This same reasoning gives us the bitmask to OR with.
We end up with:

  XXXX XXXX
| 1000 0000
-----------
  1XXX XXXX

1000 0000 in hexadecimal is 0x80.
So overall we have:

N | 0x80

While this isn't a review question, be familiar with the process to convert between binary and decimal floating point representations.