Question

We want a signed ternary representation, so we use the three’s complement representation, which is analogous to two’s complement. What is the 27-trit word representation for +34 and for -34 using three’s complement representation.

please show steps, thank you

Answer 1

Here, first we will convert the decimal value into a balaced ternary value. For this we can use long division method and then we will arrange the remainders in the reverse order.

Thus we get (34)₁₀ = (1021)₃

Now we write the 2's complement of (1021)₃ by subtracting 2 from each digit.

2's complement of 34= 01201

To get 3's complement we add 1 to 3's complement

3's complement 34= 01202

-34 can be represented similarly by making the MSB in the above representation to 1 (ie. if MSB = 1 number is negative and if MSB = 0 the number is positive)

3's complement of -34 = 11202