18. OCR GCSE (J277) 1.2 Binary shifts

Summary

This video explores binary shifts, a fundamental concept in binary arithmetic. It explains how left and right shifts move binary digits, with left shifts effectively multiplying the number by 2 and right shifts dividing it by 2. The video illustrates how bits move left or right and the effects on the binary value, using an example with the number 22. The concept is clarified by showing how shifting by more than one bit multiplies or divides by higher powers of 2, making binary shifts an efficient way to perform quick calculations.

Takeaways

• 😀 Binary shifts involve moving the bits of a binary number to the left or right.
• 😀 A left shift moves the bits one position to the left, effectively multiplying the number by 2.
• 😀 When performing a left shift, the leftmost bit disappears, and the rightmost space is filled with a 0.
• 😀 Example: Left-shifting the binary representation of 22 (10110) by 1 bit results in 44 (101100).
• 😀 A right shift moves the bits one position to the right, effectively dividing the number by 2.
• 😀 When performing a right shift, the rightmost bit disappears, and the leftmost space is padded with a 0.
• 😀 Example: Right-shifting the binary representation of 44 (101100) by 1 bit results in 22 (10110).
• 😀 Both left and right shifts can be done by more than one bit, not just by 1 bit at a time.
• 😀 Shifting left by multiple bits is equivalent to multiplying by 2 raised to the power of the number of bits shifted.
• 😀 Shifting right by multiple bits is equivalent to dividing by 2 raised to the power of the number of bits shifted.
• 😀 Binary shifts are a quick and efficient way to multiply and divide numbers by powers of 2.

Q & A

What is a binary shift?

A binary shift involves moving all the bits of a binary number to the left or right. This can either multiply or divide the number depending on the direction of the shift.

What happens when you left-shift a binary number by 1 bit?

When you left-shift a binary number by 1 bit, the bits are moved to the left, the left-most bit is discarded, and a 0 is padded on the right. This effectively multiplies the number by 2.

What is the result of left-shifting the number 22 by 1 bit?

Left-shifting the number 22 by 1 bit results in 44. The binary representation of 22 ('10110') becomes '100100', which is equivalent to 44.

How does left-shifting affect the value of the number?

Left-shifting increases the value of the number by a factor of 2 for each position shifted.

What happens when you right-shift a binary number by 1 bit?

When you right-shift a binary number by 1 bit, the bits move to the right, the right-most bit is discarded, and a 0 is padded on the left. This effectively divides the number by 2.

What is the result of right-shifting the number 22 by 1 bit?

Right-shifting the number 22 by 1 bit results in 11. The binary representation of 22 ('10110') becomes '01011', which is equivalent to 11.

How does right-shifting affect the value of the number?

Right-shifting decreases the value of the number by a factor of 2 for each position shifted.

Can you shift a binary number by more than one bit at a time?

Yes, you can shift a binary number by any number of bits. The principle is the same: bits are moved in the specified direction, and 0s are padded on the opposite side.

What is the relationship between binary shifts and multiplication/division?

A left shift multiplies the number by 2 for each bit shifted, while a right shift divides the number by 2 for each bit shifted.

Why is it useful to understand binary shifts?

Understanding binary shifts is useful because they provide a fast and efficient way to multiply and divide numbers by powers of 2, which is especially useful in computer science and programming.