Final answer:
To convert the beq, j, and jal assembly instructions into machine code, the opcodes and binary representations of the registers involved are used. The beq instruction has an opcode of 000100, the j instruction has an opcode of 000010, and the jal instruction has an opcode of 000011. The immediate value for the beq instruction is the offset from the current PC value to the target label in binary representation.
Step-by-step explanation:
The beq, j, and jal assembly instructions can be converted into machine code using their respective opcodes and binary representations of the registers involved. Here is the conversion for each instruction:
beq: The opcode for beq is 000100. The register $t0 has a binary representation of 01000 and the register $s1 has a binary representation of 10001. The immediate value is the offset from the current PC value to the target label (in this case, Loop). In this example, the offset is -4, so the binary representation of the immediate value is 11111111111111111111111111111100. Putting it all together, the machine code for the beq instruction is 000100 01000 10001 11111111111111111111111111111100.
jal: The opcode for jal is 000011. The target address calculation is the same as for the j instruction. The machine code for the jal instruction is 000011 00000001000000010000000000000011.
The student's question involves converting MIPS assembly instructions 'beq', 'j', and 'jal' to machine code. The 'beq' instruction requires calculating an offset, while 'j' and 'jal' need the target address formatted into machine code.
The student has asked to convert MIPS assembly instructions into machine code. Specifically, they want to know the binary representations for ‘beq’, ‘j’, and ‘jal’ instructions. Let's assume ‘Loop’ is at address 0x0040100C. First, we need to calculate the offset for the ‘beq’ instruction, which is done by subtracting the address of the instruction following ‘beq’ from the target address, then dividing by 4 (because MIPS instructions are 4 bytes long). So the offset for ‘beq’ is (0x0040100C - 0x00401004) / 4 = 2.
Now, we encode the instruction:
‘beq’ has an opcode of 000100. $t0 is register 8 (01000 in binary), $s1 is register 17 (10001 in binary). Thus, in machine code, ‘beq $t0, $s1, Loop’ becomes 000100 01000 10001 0000000000000010.
For ‘j’ and ‘jal’, we do not need an offset; we just need to provide the target address, which is the lower 26 bits of the address shifted right by 2 (ignoring the upper 4 bits because MIPS uses PC-relative addressing). The opcode for ‘j’ is 000010, and for ‘jal’ is 000011. If we assume an example address for ‘j’ is 0x00401000, it translates to machine code as 000010 followed by the shifted target address. The same process is applied for ‘jal’.