4.4 What does 1101₂ represent?

We have somewhat of a problem now. What value does 1101₂ represent in a 4-bit number system?

On one hand, it represents 8 + 4 + 1 = 13. However, it can also represent -C₂(1101₂) = -0011₂ = -3 (negation (-) is the same as two’s complement (C₂), so they cancel out). So, what is it?

To make this even more confusing, in a modulo-16 system, the same bit pattern also represents 29, 45, 61, and etc.

The answer is that a program chooses how to interpret the bit pattern. In assembly language programming, only very few instructions can choose how to interpret a bit pattern. This means that an add instruction does not care what values bit patterns represent. All an add instruction does is to use the logic gates described in 3.4 to derive the sum from the input bit patterns.