Why does instruction memory of IAS has 2 segments

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Each number in IAS is represented by a sign bit and a 39-bit value. Each instruction consists of an 8-bit operation code (opcode) specifying the operation to be performed and a 12-bit addressas shown in picture

So, why does instruction word has left and right side, do they corelate, can one side be executed and other not?

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why does instruction word has left and right side

It’s not actually sides, it’s 2 independent instructions. They are packed this way to save half of the space used by code.

The machine addresses 40-bit words. The instruction set is so simple, and addressable memory is so small, that it’s possible to keep 2 instructions per word.

do they corelate

Usually they run sequentially.

can one side be executed and other not?

Sometimes. If the first instruction is a jump (conditional or not), the machine will not execute the second one because it jumps instead. Similarly, jumps have 2 forms/each, one form jumps to the second instruction of the target address, when that happens, execution goes to the second instruction and the machine won’t execute the first one.