BEQ PC-Relative Branch Address Calculator

Calculate the target address for a MIPS beq instruction using PC-relative addressing.

What is PC-Relative Addressing for BEQ Instructions?

In computer architecture, specifically within MIPS processors, the beq (Branch on Equal) instruction is a fundamental control flow mechanism. It allows the program to make decisions and alter its execution path. Instead of specifying a full 32-bit absolute address to jump to, which would require a lot of space in the instruction format, beq uses PC-relative addressing. This mode calculates the target address relative to the current position of the Program Counter (PC).

This approach is efficient because most branches in programs are local, jumping to a nearby section of code. The beq instruction, being an I-type (Immediate) instruction, only has 16 bits available to encode this jump information. These 16 bits represent a signed offset, which dictates how many instructions forward or backward to jump from the current position. Our beq uses pc-relative addressing mode to calculate branch target address calculator helps you perform this exact calculation.

The BEQ Branch Target Address Formula and Explanation

The core of the calculation is a simple but specific formula that accounts for the way MIPS processors pipeline instructions. The formula is:

Target Address = (PC + 4) + (Sign-Extended Immediate << 2)

This is equivalent to:

Target Address = (PC + 4) + (Sign-Extended Immediate * 4)

Let’s break down why each component is necessary. For help with the calculation, see our guide on how to calculate branch target address mips.

Formula Variables

Variable	Meaning	Unit / Format	Typical Range
PC	The address of the current beq instruction.	32-bit Hexadecimal	Any valid memory address (e.g., 0x00400000 to 0x7FFFFFFF)
PC + 4	The address of the instruction immediately following the beq. The PC is already incremented to this by the time the branch logic is executed.	32-bit Hexadecimal	PC + 4 bytes
Immediate	The 16-bit offset value encoded in the instruction.	16-bit Signed Hex	0x0000 to 0xFFFF
Sign-Extended Immediate	The 16-bit immediate value converted to 32 bits, preserving its sign. This is crucial for handling negative offsets (backward branches).	32-bit Signed Hex	0xFFFFFFFF (-1) to 0x00007FFF (32767)
<< 2 (Multiply by 4)	The offset is multiplied by 4 because MIPS instructions are word-aligned (4 bytes each). The immediate value counts instructions, not bytes.	Arithmetic Operation	N/A

Practical Examples

Example 1: Forward Branch

Imagine a beq instruction is at address 0x00400050 and needs to jump forward by 7 instructions if the condition is met.

• Inputs:
  • PC Address: 0x00400050
  • Immediate Value: 0x0007 (for 7 instructions)
• Calculation:
  1. Calculate PC + 4: 0x00400050 + 4 = 0x00400054
  2. Sign-extend the immediate: 0x0007 becomes 0x00000007
  3. Multiply the extended immediate by 4: 7 * 4 = 28 (which is 0x1C in hex)
  4. Add the results: 0x00400054 + 0x1C = 0x00400070
• Result: The branch target address is 0x00400070.

Example 2: Backward Branch

Now, let’s consider a loop. A beq instruction is at 0x004000A0 and needs to jump back 10 instructions to repeat a block of code. For more details on MIPS branching, check out our article on the beq instruction mips.

• Inputs:
  • PC Address: 0x004000A0
  • Immediate Value: 0xFFF6 (which is the 16-bit 2’s complement representation of -10)
• Calculation:
  1. Calculate PC + 4: 0x004000A0 + 4 = 0x004000A4
  2. Sign-extend the immediate: 0xFFF6 becomes 0xFFFFFFF6 (which is -10 in 32-bit)
  3. Multiply the extended immediate by 4: -10 * 4 = -40 (which is -0x28 in hex)
  4. Add the results: 0x004000A4 - 0x28 = 0x0040007C
• Result: The branch target address is 0x0040007C.

How to Use This BEQ Branch Address Calculator

Using this calculator is straightforward. Follow these steps to determine where your program will branch.

1. Enter the Program Counter (PC): In the first input field, type the 32-bit hexadecimal address where the beq instruction is located in memory.
2. Enter the Immediate Offset: In the second field, provide the 16-bit hexadecimal immediate value that is part of the beq machine code. This value represents the number of instructions to jump, and it is treated as a signed number.
3. Review the Results: The calculator will automatically update.
   • The Branch Target Address is the final destination if the branch is taken.
   • The intermediate values show the calculation step-by-step: the value of PC+4, the immediate after sign extension, and the final byte offset.
4. Analyze the Chart: The visual chart helps you understand the direction and magnitude of the jump relative to the current instruction.

Key Factors That Affect Branch Address Calculation

• PC Value: The entire calculation is based on the starting address of the branch instruction itself. An incorrect PC value will lead to a wrong target address.
• Pipeline Effect (PC+4): The MIPS pipeline fetches the next instruction (at PC+4) before the current one is fully executed. Therefore, all relative branches are calculated from the address of the *next* instruction, not the branch instruction itself.
• Sign Extension: This is the most critical factor for backward branches (loops). Failing to sign-extend a negative immediate value will cause the calculator to compute a large forward jump instead of a short backward one.
• Word Alignment (Multiply by 4): MIPS instructions are always 4 bytes long and aligned on 4-byte boundaries. The 16-bit immediate counts *instructions* (words), so it must be multiplied by 4 to get the correct byte offset.
• 16-Bit Immediate Limit: The branch range is limited by the 16-bit signed immediate. This means a beq instruction can only jump approximately 32,767 instructions forward or 32,768 instructions backward. For longer jumps, a combination of a branch and a j (jump) instruction is needed.
• Endianness: While not a factor in the calculation itself, the way the immediate value is stored in memory (big-endian or little-endian) affects how you read it from a memory dump. This calculator assumes you have the correct logical value.

Frequently Asked Questions (FAQ)

1. Why is the offset calculated from PC+4 and not just PC?

This is due to the MIPS processor’s pipeline design. By the time the beq instruction is being decoded and its target address calculated, the PC has already been incremented to point to the next instruction in memory (at address PC+4). The hardware uses this updated PC value as the base for the offset calculation.

2. What is sign extension and why is it necessary?

Sign extension is the process of converting a smaller signed number (like our 16-bit immediate) to a larger one (32-bit) while preserving its positive or negative sign. It works by copying the smaller number’s sign bit (the most significant bit) into all the new, higher-order bits of the larger number. It’s essential for handling negative offsets, which represent backward jumps.

3. How do I represent a negative offset in hexadecimal?

You use two’s complement notation. For a 16-bit value, to get -N, you calculate 65536 - N and convert that to hex. For example, an offset of -3 is 65536 - 3 = 65533, which is 0xFFFD in hex.

4. Why do you multiply the immediate value by 4?

The immediate value in a MIPS branch instruction represents the number of *instructions* (or words) to jump. Since each MIPS instruction is 4 bytes long, we must multiply the offset by 4 to convert it into a byte-based offset that can be added to the byte-based PC address.

5. What is the maximum distance a `beq` instruction can branch?

The 16-bit signed immediate allows for a range of -32,768 to +32,767. Since this is an instruction (word) offset, the maximum byte range is -32768 * 4 to 32767 * 4, which is -131,072 bytes to +131,068 bytes from the PC+4 address.

6. What happens if the values in the two registers are not equal?

If the values in the two source registers being compared by beq are not equal, the branch is “not taken.” The processor simply discards the target address calculation and proceeds to execute the instruction at PC+4, continuing sequentially.

7. Can I enter decimal numbers in the calculator?

No, this specific calculator is designed for users working with assembly and machine code, where addresses and instruction components are almost always represented in hexadecimal. You must convert any decimal values to hex before using the tool.

8. What is the difference between this and a `j` (jump) instruction?

A beq instruction is a *conditional branch* with a limited range that uses PC-relative addressing. A j instruction is an *unconditional jump* that uses a different format (J-type) to specify a 26-bit pseudo-absolute address, allowing it to jump to a much larger range of memory locations within a 256MB segment.