Question

A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction word has an opcode, two register operands and am immediate operand. The number of bits available for the immediate operand field is ______. 

Answer 1

40 distinct instructions → log₂40 = 6 bits are needed for opcode.

24 general purpose registers → log₂ 24 = 5 bits for register operand.

As, two register operands are required so, total 10 bits are needed for register operand field.

Suppose for immediate operand we require x bits.

Opcode	Register operand	Immediate operand
6 bits	10 bits	x bits

Opcode + Register operand + Immediate operand = 32

6 + 10 + x = 32

∴ x = 16

Number of bits available for the immediate operand field (x) is 16 bits.