Binary Shifts (Cambridge International IGCSE Computer Science)

Spec point — 1.1.5 · "5 Perform a logical binary shift on a positive 8-bit binary integer and understand the effect this has on the positive binary integer"

Binary Shifts

What is a logical binary shift?

Exam Hint Cambridge IGCSE 0478 expects you to perform binary shifts on 8-bit values and explain how the result changes (×2, ÷2). Every example here mirrors the real exam format.

• A logical binary shift is how a computer system performs basic multiplication and division on non-negative values (0 and positive numbers)
• 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 logical left shift of 1?

• Here is the binary representation of the denary number 40

• To perform a left logical binary shift of 1, we move each bit 1 place to the left
• Since the most significant bit is 0, there is no overflow
• The 1 column becomes empty so is filled with a 0

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

How do you perform a logical 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 places to the left
• Since the two leftmost bits are 0, nothing important is lost and no overflow occurs
• The 1 and 2 column become empty so are filled with a 0

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

Exam Hint Your textbook might show shifts with longer binary values—but in IGCSE exams, you’ll only ever be asked about 8-bit unsigned integers. That’s why all our examples are capped at 8 bits.

How do you perform a logical 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 bit in the 1 column (LSB) is shifted out and lost
• The 128 column becomes empty so is filled with a 0

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

How do you perform a logical 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 bits in the 1 and 2 columns are shifted out and lost
• The 128 and 64 columns become empty so are filled with a 0

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

Overflow in binary shifts

• Overflow happens when a 1 is shifted out of the most significant bit (MSB) on the left in a logical left shift
• This means important data is lost, which can seriously change the number’s value

Exam Hint In IGCSE Computer Science, you usually only need to spot an overflow when a 1 is shifted out on the left. You don’t need to worry about underflow in this context!