Data Representation: Number Systems: Perform A Logical Binary Shift On A Positive 8-bit Binary Integer And Understand The Effect This Has On The Positive Binary Integer (Copy)
| Concept | Logical Binary Shift (Positive 8-bit Integer) |
|---|---|
| Definition | A logical binary shift moves all bits in a binary number left or right, filling empty positions with 0, without preserving sign. |
| Applies To | Positive 8-bit binary integers only (no sign bit interpretation). |
| Bit Length | Always 8 bits before and after the shift. |
| Fill Rule | Vacated positions are filled with 0. |
| Bits Lost | Bits shifted out of the 8-bit range are discarded permanently. |
| Type Of Shift | Operation | Effect On Value | Key Exam Point |
|---|---|---|---|
| Logical Left Shift (<<) | All bits move left by n positions | Value multiplies by 2ⁿ (if no overflow) | Rightmost bits become 0 |
| Logical Right Shift (>>) | All bits move right by n positions | Value divides by 2ⁿ (integer division) | Leftmost bits become 0 |
| Example | Binary | Decimal |
|---|---|---|
| Original Value | 00110110 | 54 |
| Left Shift by 1 | 01101100 | 108 |
| Right Shift by 1 | 00011011 | 27 |
| Step | Logical Left Shift (1 Place) |
|---|---|
| 1 | Write original 8-bit binary number |
| 2 | Move every bit one position to the left |
| 3 | Drop the leftmost bit if overflow occurs |
| 4 | Insert 0 at the rightmost position |
| Step | Logical Right Shift (1 Place) |
|---|---|
| 1 | Write original 8-bit binary number |
| 2 | Move every bit one position to the right |
| 3 | Drop the rightmost bit |
| 4 | Insert 0 at the leftmost position |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Computer Science Full Scale Course
| Shift Amount | Mathematical Effect (If No Overflow) |
|---|---|
| Left Shift by 1 | ×2 |
| Left Shift by 2 | ×4 |
| Right Shift by 1 | ÷2 |
| Right Shift by 2 | ÷4 |
| Overflow | Meaning |
|---|---|
| When it occurs | A bit is pushed beyond the 8-bit limit |
| Result | Data loss and incorrect value |
| Exam Warning | Always mention overflow if shown or implied |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Computer Science Full Scale Course
| Key Properties | Logical Binary Shift |
|---|---|
| Sign Bit Handling | No sign bit consideration |
| Suitable For | Fast multiplication/division by powers of 2 |
| Data Preservation | Not preserved if overflow occurs |
| Use In Exams | Data manipulation, efficiency questions |
| Common Examiner Traps | How To Avoid |
|---|---|
| Forgetting to keep 8 bits | Always rewrite result as 8-bit |
| Using sign extension | Logical shift always inserts 0 |
| Ignoring overflow | Mention lost bits explicitly |
| Treating as arithmetic shift | Logical ≠ arithmetic |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Computer Science Full Scale Course
| One-Line Summary | Exam-Perfect Statement |
|---|---|
| Logical Left Shift | Moves bits left, fills with 0, multiplies value |
| Logical Right Shift | Moves bits right, fills with 0, divides value |
| Overflow | Causes permanent data loss |
Written and Compiled By Sir Hunain Zia (AYLOTI), World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Computer Science Full Scale Course