Question

2.23 Suppose the program counter (PC) is set to 0x2000 0000

2.23.1 [5] <§2.10> What range of addresses can be reached using the LEGv8 branch (B) instruction? (In other words what is the set of possible values for the PC after the branch instruction executes?)
2.23.2 [5] <§2.10> What range of addresses can be reached using the LEGv8 conditional branch-on-equal (CBZ) instruction? (In other words what is the set of possible values for the PC after the branch instruction executes?)

Answer 1

The signed offset can be positive or negative, and the resulting PC will fall within the range:

`\(0x2000 0000 + (\text{{signed offset}} \, \text{{shifted left by 2 bits}})\).`

2.23.2. The PC is updated similarly to the branch instruction:
`\(0x2000 0000 + (\text{{signed offset}} \, \text{{shifted left by 2 bits}})\)` if the specif

The LEGv8 branch (B) instruction is known to be an unconditional branch

In terms of 2.23.1: LEGv8 Branch (B) Instruction, The range of addresses reachable using the LEGv8 branch (B) instruction from a PC of 0x2000 0000 is determined by the signed offset. The formula for the updated PC is
`\(0x2000 0000 + (\text{{signed offset}} \, \text{{shifted left by 2 bits}})\).`

In terms of 2.23.2: LEGv8 Conditional Branch-on-Equal (CBZ) Instruction

The range of addresses reachable using the LEGv8 conditional branch-on-equal (CBZ) instruction is also determined by the signed offset. The PC is updated similarly to the branch instruction:

`\(0x2000 0000 + (\text{{signed offset}} \, \text{{shifted left by 2 bits}})\)` if the specified register contains zero; otherwise, the PC remains unchanged.

So, both the branch (B) and CBZ instructions in LEGv8 can be able to get to the addresses within the range set by the signed offset added to the initial value of the program counter