no of 0 address instructions

Question

A hypothetical processor supports two-address, one-address and zero-address instructions. It has a 256 word memory and each instruction is 19 bits long. If there are 4 two-address instructions and 1000 one-address instructions, how many zero-address instructions are there?( Marks: 0.00 )

1.   5126
2.   2048
3.   1024
4.   6144

Answer 1

Explanation:
Since it is a 256 (= 2^8) word memory the no. of bits needed to address the memory = 8

Since each instruction is of length 19-bits, a two-address instruction can be divided as 8+8+3 where 8 bits for 1st-address , 8 bits for 2nd-address and 3-bits for opcode.

Also with 19 bits for an instruction giving 2^19 possible encodings.

It is given there are 4 two-address instructions, so no. of encodings for two-address instructions = 4 * 2^8 * 2^8 = 4*2^16

Also there are 1000 one-address instructions, so no. of encodings for one-address instructions = 1000 * 2^8

Then total number of possible 0-address instructions = 2^19 - (4*2^16 + (1000 * 2^8) )

= 2^8 * (2^11 - 4*256 - 1000)
= 2^8 *(2048-2024)
= 256*24
= 6144

Comments

@mohit my doubt is why we can not encode 1000 instructions with log(1000) bits? why we have to take 1000 bits

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for what will be the 8 bit address field used in instructions.

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because the total $1000$ number of one address instruction is there, it is not an address field.

Answer 2

4th that 6144 is the answer...

total number of zero address instructions possible....

2^19=524288....

now for creation of 1 address and 2 address we will eat up bits from o address instruction...

now 1 address instruction will eat up combinations =1000*(2^8)...reason = 1 address contain one memory refrence...so 8 bits for one refrence...such thousand instructions are needed...so we get it as 1000*(2^8)=256000....

now 2 address instructions...same as above....4*(2^16)=262144.....

hence remaining zero address=524288-256000-262144..=6144..

Comments

total number of zero address instructions possible....

2^19=524288....

This is the total number of instructions possible not total number of ZERO instructions right?

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yes...zero address means all bits dedicated to OPCODE....so if system support ONLY zero address then

it would be correct...i just misplace the words...