3.04 - Binary Shifts

Multiplying or dividing by powers of 10 (10, 100, 1000, ...) in base-10 (decimal) is really easy.
The same goes for powers of 2 (2, 4, 8, ...) in base-2 (binary)

To multiply by 2 in binary, we add a 0 on the end of the number (just like multiplying by 10 in decimal):
• two times 1011₂ is 10110₂
• two times 11111111₂ is 111111110₂

To multiply by 4, we multiply by 2 twice (add two 0s on the end: just like multiplying by 100 in decimal).

A binary left-shift is equivalent to adding 0s on the end of a binary number.

For example, left-shifting the number 1101₂ by two places would give us 110100₂. Two zeros have been added to the end.

A number is doubled every time it is left-shifted by one place. This means that left-shifting a number by two places would multiply it by 4.

A binary right-shift is equivalent to taking away digits from the end of a binary number.

For example, right-shifting the number 1101₂ by two places would give us 11₂. The last two digits have been removed.

A number is halved every time it is right-shifted by one place. This means that right-shifting a number by two places would divide it by 4.

NOTE: if you right-shift an odd number, it will round down after halving. This is like the integer division (DIV) operator that was discussed in 2.03 (Operations).

What is the numerical result (in terms of multiplication or division) of left-shifting a number three places?

Multiply by 2³ = 8.