*CS:APP* is a textbook about computer systems through the language C. This is the start of my journey attempting the fundamentals of software, peeling away layers of abstraction in higher-level implementations. My ultimate goal is to build a small but working operating system.
# Chapter 1: A Tour of Computer Systems
*Omitted*
# Chapter 2: Representing and Manipulating Information
## Mask
`&` is the bitwise masking operation.
## Bitwise Operations & Logic Operations
Bitwise and logical operations differ in their scope. Bitwise operators operate "bitwise". While logical operators treat entire arguments as a single `True` or `False`, if the argument is non-zero or zero.
| Logical (English) | Bitwise | Logical |
| ----------------- | ------- | ------- |
| NOT | ~ | ! |
| AND | & | && |
| OR | \| | II |
| XOR | ^ | |
For example:
1. `a&!b = 0x00` for any `b`$\ne$ `0x00`.
2. `(~a|~b)`$\ne$ `~(a|b)` Because `|` works on both when the two bits are both 1 or either one is 1. It is not distributive.
3. In fact, `~` is not distributive over any bitwise operations. Some meaningful relations may be `&` and `|` are distributive over each other, and `(~a^~b)`$=$ `a^b`.
4. To express the `==` sign in `a==b` with bitwise and logical operations: `!(a^b)`
## Shift Operations
`<<` and `>>` perform left and right shift to bits. After shifting the data, logical shifts fill the gap with `0`s, while arithmetic shifts fill the gap with the most significant bits. There are no left arithmetic shifts (because arithmetic shifts are used the preserve the sign bit). In C standards, there is no constraint over arithmetic or logical shift for signed data (but it does enforce logical shift for unsigned data). In Java, they are specified by `<<<` for logical and `<<` for arithmetic.
Addition and subtraction has higher precedence than shift.
Note the answer key for practice problem 2.16 in the Global Edition of *CS:APP* is **wrong** for some of the arithmetic shifts.
C avoid overflowing when shifting by a `k>w`. It masks `k` to only the lower $log_g w$ bits, that is.
```c
k mod w = k & (w-1)
```
given $w \in \{ 2^{n} \mid n \in \mathbb{N}\}.$
CS:APP is a textbook about computer systems through the language C. This is the start of my journey attempting the fundamentals of software, peeling away layers of abstraction in higher-level implementations. My ultimate goal is to build a small but working operating system.
Chapter 1: A Tour of Computer Systems
Omitted
Chapter 2: Representing and Manipulating Information
Mask
&is the bitwise masking operation.Bitwise Operations & Logic Operations
Bitwise and logical operations differ in their scope. Bitwise operators operate “bitwise”. While logical operators treat entire arguments as a single
TrueorFalse, if the argument is non-zero or zero.a&!b = 0x00for anyb=0x00.(~a|~b)=~(a|b)Because|works on both when the two bits are both 1 or either one is 1. It is not distributive.~is not distributive over any bitwise operations. Some meaningful relations may be&and|are distributive over each other, and(~a^~b)=a^b.==sign ina==bwith bitwise and logical operations:!(a^b)Shift Operations
<<and>>perform left and right shift to bits. After shifting the data, logical shifts fill the gap with0s, while arithmetic shifts fill the gap with the most significant bits. There are no left arithmetic shifts (because arithmetic shifts are used the preserve the sign bit). In C standards, there is no constraint over arithmetic or logical shift for signed data (but it does enforce logical shift for unsigned data). In Java, they are specified by<<<for logical and<<for arithmetic.Addition and subtraction has higher precedence than shift.
Note the answer key for practice problem 2.16 in the Global Edition of CS:APP is wrong for some of the arithmetic shifts.
C avoid overflowing when shifting by a
k>w. It maskskto only the lower loggw bits, that is.given w∈{2n∣n∈N}.
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