From 2a262d36bf10e6ed2aac0952433c6f7ccad77da1 Mon Sep 17 00:00:00 2001
From: anebz <anebzt@protonmail.com>
Date: Tue, 7 Apr 2020 18:55:21 +0200
Subject: [PATCH] 5.5. debugger

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 05. Bit manipulation/5.5. Debugger.md | 57 +++++++++++++++++++++++++++
 README.md                             |  1 +
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 create mode 100644 05. Bit manipulation/5.5. Debugger.md

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+# 5.5. Debugger
+
+> Explain what the following code does: (( n & (n-1)) == 0)
+
+```c++
+  00000010   (n)
+& 00000001   (n - 1)
+----------
+  00000000
+```
+
+n should be odd. And if it's bigger than 2, it'll have some 1s higher up. Which won't be cleared when doing n-1. so n must be 2.
+
+## Hints
+
+> Start with a brute force solution. Can you try all possibilities?
+
+n=2, but there must be something more.
+
+> What does it mean if A & B == 0?
+
+That A and B don't have any same bits in any position.
+
+> If A & B == 0, then it means that A and B never have a 1 at the same spot. Apply this to the equation in the problem.
+
+A and B are separated by 1 bit in this case, A = B + 1. It could be all 0s and 10 in the end (n=2), or 100000. So that n = pow(2,x). A power of 2.
+
+```c++
+  10000000   (n)
+& 01111111   (n - 1)
+----------
+  00000000
+```
+
+> If ( n & ( n-1)) == 0, then this means that n and n - 1 never have a 1 in the same spot. Why would that happen?
+
+When n is a power of 2.
+
+> What is the relationship between how n looks and how n - 1 looks? Walk through a binary subtraction.
+
+Yes.
+
+> When you do a binary subtraction, you flip the rightmost 0s to a 1, stopping when you get to a 1 (which is also flipped). Everything (all the 1 s and Os) on the left will stay put.
+
+Same answer.
+
+> Picture n and n - 1. To subtract 1 from n, you flipped the rightmost 1 to a 0 and all the 0s on its right to 1s. If n & n -1 == 0, then there are no 1 s to the left of the first 1. What does that mean about n?
+
+I'm getting lost.
+
+> We know that n must have only one 1 ifn & ( n -1) == 0. What sorts ofnumbers have only one 1?
+
+Powers of 2! Or the binary base number.
+
+## Solution
+
+Correct! n = a power of 2, or n=0.
diff --git a/README.md b/README.md
index e2aa410..caad832 100644
--- a/README.md
+++ b/README.md
@@ -54,6 +54,7 @@ If you can't afford to buy the book, you can find a free pdf [here](http://ahmed
 * Insert bit
 * Binary to string
 * Flip bit to create longest sequence of 1s
+* (( n & (n-1)) == 0). n=?
 
 ## Chapter 7 Object-oriented design