A processor uses a 32-bit instruction format and supports byte-addressable memory access. The ISA of the processor has 150 distinct instructions. The instructions are equally divided into two types, namely R-type and I-type, whose formats are shown below.
R-type Instruction Format:
In the OPCODE, 1 bit is used to distinguish between I-type and R-type instructions and the remaining bits indicate the operation. The processor has 50 architectural registers, and all register fields in the instructions are of equal size.
Let 𝑋 be the number of bits used to encode the UNUSED field, 𝑌 be the number of bits used to encode the OPCODE field, and 𝑍 be the number of bits used to encode the immediate value/address field. The value of 𝑋 + 2𝑌 + 𝑍 is ________