Question

5. a.) Design an Expanding Opcode to allow all the following to be encoded in a 16-bit instruction:

4 instructions with two 5-bit addresses and one 3-bit register number

15 instructions with one 5-bit address and one 3-bit register number

31 instructions with no addresses or registers

(Specify the bit organization and the beginning opcode and ending opcode for each category.)

b.) Design an Expanding Opcode to allow all the following to be encoded in a 36-bit instruction:

7 instructions with two 15-bit addresses and one 3-bit register number

500 instructions with one 15-bit address and one 3-bit register number

40 instructions with no addresses or registers

(Specify the bit organization and the beginning opcode and ending opcode for each category.)

Answer 1

Answer:-----------
5. a).
The first format consists of a 3-bit opcode, two 5-bit address fields, and one 3-bit register field. The 3-bit opcode allows for 4 instructions and one opcode for “expansion”.

The second format consists of a 3-bit fixed “extended” opcode field, 5-bits for the extended opcode, one 5-bit address field, and one 3-bit register field. The 5-bit extended opcode allows 32 unique instructions, which easily contains the required 15 instructions.

The third format consists of a 3-bit fixed “extended” opcode field, a fixed 5-bit “extended-extended” opcode field, and 8-bits for additional instructions. Alternately, the second format had plenty of opcodes available to define 31 instructions where the address and register fields would be ignored.

Format 1	Opcode, 3-bits 4 instructions 000 - 011	Address 5 bits	Address 5 bits	Register 3-bits
Format 2	Expanding Opcode Basis 100	Expanding Opcode 5 bits 15 of 32 used	Address 5 bits	Register 3-bits
Format 3	Expanding Opcode Basis 100	Expanding Opcode 5 bits 31 of 32 used	Unused	Unused

5. b).
The first format consists of a 3-bit opcode, two 15-bit address fields, and one 3-bit register field. The 3-bit opcode allows for 7 instructions and one opcode for “expansion”.

The second format consists of a 3-bit fixed “extended” opcode field, 15-bits for the extended opcode, one 15-bit address field, and one 3-bit register field. The 15-bit extended opcode allows 32,768 unique instructions, which easily contains the required 500 instructions.

The third format consists of a 3-bit fixed “extended” opcode field, a fixed 15-bit “extended-extended” opcode field, and 18-bits for additional instructions. Alternately, the second format had plenty of opcodes available to define 40 instructions where the address and register fields would be ignored.

Format 1	Opcode, 3-bits 7 instructions 000 - 110	Address 15 bits	Address 15 bits	Register 3-bits
Format 2	Expanding Opcode Basis 111	Expanding Opcode 15 bits 500 of 32,768 used	Address 15 bits	Register 3-bits
Format 3	Expanding Opcode Basis 111	Expanding Opcode 15 bits 40 of 32,768 used	Unused	Unused