Question

In class, we talked about the unsigned number representation, where each bit of a number has the following values:

+32 + 16 +8 +4 +2 +1

We also talked about the two's complement representation, which is as follows:
-32 + 16 +8 +4 +2 +1

And we also talked about sign magnitude:
sign +16+8 +4 +2 +1

Professor Fuzzybrain (not here at CPP) has proposed a triplex number representation, where each bit has the following values:
-9 +9 -3 +3 -1 +1

Using triplex, the bit pattern 000110 represents the number 2(+3 plus -1), and the bit pattern 100001 represents −8(−9 plus +1). Using 6-bit triplex, answer the following questions:
A. What is the largest value that can be represented, and what is its bit pattern?

Answer 1

The largest value that can be represented in triplex number representation with a 6-bit configuration is 13, which corresponds to the bit pattern 010101.

Step-by-step explanation:

To find the largest value that can be represented in triplex number representation using a 6-bit configuration with bit values assigned as -9, +9, -3, +3, -1, +1, we must maximize the positive contributions of the bits. Signalizing that the positive bits should be set to 1 and the negative bits should be set to 0, to avoid subtracting from the total value. The bit pattern for the largest value would be 010101, which corresponds to the sum +9 +3 +1 = 13. Therefore, the largest value that can be represented is 13, with the bit pattern 010101.