GATE CS 1998 Q1.17 — Number Representations (Fixed and Floating Point)

To find the decimal equivalent of the octal number $(342)_8$ when treated as an 8-bit signed integer on an 8085-based computer, we follow these steps:

Step 1: Convert the octal number to binary
Each octal digit is represented by 3 bits:

• $3 \to 011$
• $4 \to 100$
• $2 \to 010$

Step 2: Represent as an 8-bit integer
Since the 8085 is an 8-bit processor, we take the 8 least significant bits (LSBs):$$\text{8-bit representation} = 11100010_2$$

Step 3: Determine the decimal value
In the 8085 microprocessor, signed integers are represented in 2's complement form. Since the most significant bit (MSB) is $1$, the number is negative.

To find its magnitude, we take the 2's complement of $11100010_2$:

1. Find the 1's complement: $00011101_2$
2. Add $1$: $00011101_2 + 1 = 00011110_2$

Since the original MSB was $1$, the decimal equivalent is $-30$.

Therefore, the correct option is D.