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Concept

Overview

AND · OR · XOR · shifts · the classic tricks
step 1 / 6
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The bit toolkit
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1// bit b worth 2^position
2x & y   // 1 where both 1   (mask / test)
3x | y   // 1 where either   (set bits)
4x ^ y   // 1 where differ   (x^x=0, x^0=x)
5x << k  // shift up (×2^k);  1<<k = bit-k mask
6n & (n-1)  // clears the lowest set bit
state
  • value5
  • binary0101
  • places8 4 2 1

line 1Every integer is a string of BITS, each worth a power of two: positions (left→right here) are 8, 4, 2, 1. 5 = 0101 = 4 + 1. Bit tricks manipulate these directly with the operators &, |, ^, ~, and the shifts << / >>.