Section 2.6 – Logical Operations in LEGv8

1. Why Logical Operations Exist

• Early computers operated on whole words.
• It became clear it was useful to operate on fields of bits within a word or on individual bits.
• Example: examining characters within a word (each character = 8 bits).
• Programming languages and ISAs added logical operations to simplify:
  • Packing/unpacking bits.
  • Isolating fields.
  • Masking bits.

2. Common Logical Operations: C, Java, LEGv8 Mapping

3. Shifts

3.1 Concept

• A shift moves all bits in a doubleword left or right.
• Emptied bits are filled with 0s.
• LEGv8 instructions:
  • LSL = Logical Shift Left.
  • LSR = Logical Shift Right.
  • “Shift left logical provides a bonus benefit. Shifting left by i bits gives the same result as multiplying by 2i, just as shifting a decimal number by i digits is equivalent to multiplying by 10i. For exammmmjmmj7ple, the above LSL shifts by 4, which gives the same result as multiplying by 2^4 or 16. The first bit pattern above represents 9, and 9 × 16 = 144, the value of the second bit pattern.”
  • Shamt stands for shift amount in our previously explained R-format

3.2 Example – Shift Left by 4

• Initial value (decimal 9):

00000000 00000000 00000000 00000000 00000000 00000000 00000000 00001001