Module 5: Unconditional Branches - Detailed Notes

Module 5: Unconditional Branches

Objectives

• Perform hexadecimal addition and subtraction.

• Use unconditional branch and jump instructions.

Lecture Outline

• Instructions

• Hexadecimal Addition and Subtraction

• Extending Hexadecimal Numbers

• Truncating Hexadecimal Numbers

• Relative Addressing (REL with 8-bit signed offset)

• Calculating Branch Destinations

• Relative Addressing (REL with 16-bit signed offset)

• JUMP Instruction

Instructions

• BRA, LBRA: Always branch to an instruction, uses relative addressing.

• BRN, LBRN: Never branch to an instruction, uses relative addressing.

• JMP: Jump to an instruction at a specified address, uses extended or indirect addressing.

Hexadecimal Addition and Subtraction

• Adding and subtracting in hexadecimal is similar to decimal arithmetic.

• Carries and borrows are worth 16 instead of 10.

• Example 5.1: $2367 + 5FD6$

• Example 5.2: $AC22 - 1EE8$

Extending Hexadecimal Numbers

• When adding or subtracting numbers with different lengths, the shorter number must be extended to match the longer number's number of digits.

• Unsigned Extension:

  • Example 5.3: $2357 + D6$

• Signed Extension:

  • Example 5.4:

    • a) $2357 + D6$

    • b) $2357 + 6D$

Truncating Hexadecimal Numbers

• Microcomputers often use a fewer number of bits to represent values to save time and space.

• The process of extending numbers can be reversed with care.

• Unsigned Truncation:

  • Example 5.5: Truncate each 16-bit value to an 8-bit value or state that it is not possible.

    • a) $00F5$

    • b) $10EC$

• Signed Truncation:

  • Example 5.6: Truncate each 16-bit value to an 8-bit value or state that it is not possible.

    • a) $0045$

    • b) $00F5$

    • c) $FFD1$

    • d) $FF66$

    • e) $F280$

Relative Addressing (REL with 8-bit signed offset)

• Effective Address Calculation: Add the operand (as a signed number) to the value in the Program Counter (PC).

• The effective address is then loaded into the PC, and the program executes from that new address.

• Format: One-byte hexadecimal value representing a signed value.

• Example 5.7:

  • a) BRA $30$

  • b) BRA $-10$

• The value entered into machine code is the number of bytes forward or backward from the byte after the entire branch instruction, including the operand.

Calculating Branch Destinations

• The change in the Program Counter is calculated as: $Final Value – Initial Value$.

• Determine if the result can be represented as a one-byte signed value.

• Example 5.8: Calculate the offset to the destination specified from the BRA instruction starting at address $2000h$.

  • a) Initial Address: $2000$, Destination: $2060$

  • b) Initial Address: $2000$, Destination: $2085$

  • c) Initial Address: $2000$, Destination: $1FF0$

  • d) Initial Address: $2000$, Destination: $1F80$

Relative Addressing (REL with 16-bit signed offset)

• Effective Address Calculation: Add the operand (as a signed number) to the value in the PC.

• The effective address is loaded into the PC, and the program executes from that new address.

• Format: Two-byte hexadecimal value representing a signed value.

• Example 5.9:

  • a) BRA $3000$

  • b) BRA $-1000$

• Machine code represents the number of bytes forward or backward from the byte after the branch instruction (including the operand).

• With a 16-bit offset, all memory addresses are reachable, so the offset calculation is always valid.

JUMP Instruction

• Key Difference Between JUMP and BRANCH:

  • Branch: Uses a relative offset based on the current value of the Program Counter (PC).

  • Jump: Executes the next instruction at a fixed, known address or at a relative offset from an index register; it does not depend on the value of the PC.

• Branches are generally preferred over jumps.

• Conditional branches enable the process to make decisions by continuing execution or branching to a different instruction (covered in the next module).

• Code should be address agnostic, meaning it does not need to be loaded to a specific starting address to function correctly.

• Example 5.10: Write an instruction to cause the processor to start executing at address $4500$, regardless of the instruction's location in memory.