Binary Shifts (AQA GCSE Computer Science)

Binary Shifts

What is a binary shift?

• A binary shift is how a computer system performs basic multiplication and division

• Binary digits are moved left or right a set number of times

• A left shift multiplies a binary number by 2 (x2)

• A right shift divides a binary number by 2 (/2)

• A shift can move more than one place at a time, the principle remains the same

• A left shift of 2 places would multiply the original binary number by 4 (x4)

How do you perform a left shift of 1?

• Here is the binary representation of the denary number 40

• To perform a left binary shift of 1, we move each bit 1 place to the left

• The digit in the 128 column will move left causing an overflow error

• The 1 column becomes empty so is filled with a 0

• The original binary representation of denary 40 (32+8)  has multiplied by 2 and became 80 (64+16)

How do you perform a left shift of 2?

• Here is the binary representation of the denary number 28

• To perform a left binary shift of 2, we move each bit 2 place to the left

• The digit in the 128 and 64 column will move left causing an overflow error

• The 1 and 2 column become empty so are filled with a 0

• The original binary representation of denary 28 (16+8+4)  has multiplied by 4 and became 112 (64+32+16)

How do you perform a right shift of 1?

• Here is the binary representation of the denary number 40

• To perform a right binary shift of 1, we move each bit 1 place to the right

• The digit in the 1 column will  move right causing an underflow error

• The 128 column becomes empty so is filled with a 0

• The original binary representation of denary 40 (32+8)  has divided by 2 and became 20 (16+4)

How do you perform a right shift of 2?

• Here is the binary representation of the denary number 200

• To perform a right binary shift of 2, we move each bit 2 places to the right

• The digits in the 1 and 2 columns will move right causing an underflow error

• The 128 and 64 columns become empty so are filled with a 0

• The original binary representation of denary 200 (128+64+8) has divided by 4 and became 50 (32+16+2)