Show understanding of and perform binary shifts

4.3 Bit Manipulation 🚀

🔍 What is Bit Manipulation?

Bit manipulation is like playing with LEGO bricks, but each brick is a single 0 or 1. By moving, adding, or removing these bricks we can change numbers in clever ways.

🔄 Binary Shifts

Shifting moves all bits left or right, just like sliding a row of dominoes.

• Left shift (<<) moves bits to the left, adding zeros on the right.
• Right shift (>>) moves bits to the right, discarding bits on the right.

🔢 Left Shift Example

Take the 8‑bit number 0001 0101 (decimal 21). Shift left by 2 positions:

0001 0101 << 2 = 0101 0100

In decimal, $21 \times 2^2 = 84$.

🔢 Right Shift Example

Take 0101 0100 (decimal 84). Shift right by 3 positions:

0101 0100 >> 3 = 0000 1010

In decimal, $84 \div 2^3 = 10$.

⚖️ Arithmetic vs Logical Shift

When shifting right, the sign bit (leftmost bit) can be preserved (arithmetic) or replaced with 0 (logical).

💡 Practical Uses

1. Fast multiplication/division by powers of two.
2. Bit masks for setting, clearing, or toggling specific bits.
3. Efficient algorithms in graphics and cryptography.

📝 Quick Quiz

What is the result of 1010 0011 << 1?

• A) 0100 0110
• B) 1010 0110
• C) 0100 1100
• D) 1010 0011

Answer: B (shift left adds a 0 on the right).

📌 Summary

Shifting is a powerful tool that lets you multiply or divide by 2, 4, 8… instantly, and it’s a key part of many low‑level programming tricks.