Question

5. Suppose we have a 32-bit computer with an instruction set that supports immediate instructions as shown below:

Opcode Source Register Destination Register immediate

6 bits 5 bits 5 bits 16 bits

(a) How many registers at most does this computer have? (5%)

(b) How many operations at most can this computer have? (5%)

(c) What is the range of the number in the “immediate” field in 2'scomplement format? (5%)

Answer 1

SOL:

Given computer = 32 bits

Opcode = 6bits

Source Register = 5 bits

Destination Register = 5 bits

Immediate field = 16bits

a) The no of register the computer have = 2^{no of register bits}

here Source Register = 5 bits, Destination Register = 5bits

5 bits are allocated for registers

No of register bits = 5

The no of registers the computer have = 2⁵ = 32

so No of registers = 32

b) The no of operations the computer have = 2^{no of bits in opcode}

= 2⁶

= 64

so No of operations the computer have = 64

c) Given immediate field = 16 bits

The range of 2^'s complement format of n bits = -2^n-1 to +(2^n-1 -1)

The range of number in immediate field in 2's complement format is = -2^16-1 to +(2^n-1 -1)

= -2¹⁵ to +(2^16-1 -1)

= -2¹⁵ to +(2¹⁵ -1)

= -32,768 to 32,767