complement many

notes/1.md

@@ -1,9 +1,55 @@
 
 # Bits, Bytes, and Integers
 
+In computers, everything consists of bits.
+By encoding sets of bits in various ways, they made meanings:
+
+* instructions
+* and data(numbers, sets, strings, etc..)
+
+## Boolean Algebra
+
+* and `A & B`
+* or `A | B`
+* not `~A`
+* xor `A ^ B`
+
+### in C
+
+* Shift (`<<`, `>>`)
+  * Left Shift(`<<`)
+  Zero fill on right
+  * Right Shift(`>>`)
+  Logical Shift: zero fill with 0's on left
+  Arithmetic shift Relicate most significant bit on left
+
+```c {cmd="gcc" args=[-x c $input_file -O0 -m32 -o 1_1.out]}
+#include <stdio.h>
+
+int main() {
+  int a = 0x7fffffff;
+  int as = a << 1;
+  printf("shl of %d: %d(%08x)\n", a, as, as);
+  
+
+  unsigned b = 0x7fffffff;
+  unsigned bs = b << 1;
+  printf("shl of %u: %u(%08x)\n", b, bs, bs);
+}
+```
+
+```sh {cmd hide}
+while ! [ -f 1_1.out ]; do sleep .1; done; ./1_1.out
+```
+
 ## Integers
 
-### Representation
+### Representation & Encoding
+
+* for $w$ bits data $x$
+
+$$B2U(X)=\sum_{i=0}^{w-1} x_i 2^{i}\quad B2T(X)=-x_{w-1}*2^{w-1} + \sum_{i=0}^{w-2}{x_i 2^i}$$
+
 
 ### Conversion