Shifting Bytes, Quicker Arithmetic

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Byte shifting

Introduction

Shifting or byte shifting is a process of shifting bytes of a given binary number in ether left or right direction. In programming shifting is marked by the shift operator:

• Right shifting, decalage a droite >>
• Left shifting, decalage a gauche <<

EXEMPLE

Consider the octet / byte : 00111000

00111100 >> 1 -> 00011110
00111100 << 1 -> 01111000

In this exemple we shifted the binary 00111100 by one bit in both left and right direction.

DANGER

shifting is a lossy operation data can be lost as it does NOT create more bit, it just move them in a direction right/left a cut of whatever fall out of the initial encoding.

Arithmetic and byte shifting

In a given base b, where b represent the number of symbol used to count. shifting by n is equivalent to multiply by $b^n$.

Formula :

$$\text{For }x\in \text{Base }b⟹\{\begin{array}{l}x\text{ >> }n=x÷b^n\\ x\text{ << }n=x\times b^n\end{array}$$

It’s more striking in binary as with the naked eye, we can observe this formula.

Decimal	Binary
1	1
2	10
4	100
7	111
14	1110
28	11100

NOTE

Multiplying by 2 is the same as shifting by left by one