Question

Which of the following systems are used to represent both positive and negative numbers? \[ \begin{aligned} (a)&\ \text{Sign-and-magnitude} (b)&\ \text{Sign-9's complement} (c)&\ \text{1's complement} (d)&\ \text{Sign-10's complement} \end{aligned} \]

• (a) and (c)
• (a) and (b)
• (b) and (d)
• (c) and (d)

Hint:

Common signed-number systems:
• Sign-and-Magnitude
• 1's Complement
• 2's Complement Modern computers mostly use 2's Complement representation.

Answer 1

The Correct Option is A

Concept: Computers must represent both positive and negative numbers using binary digits. Several signed-number representation techniques exist:
• Sign-and-Magnitude
• 1's Complement
• 2's Complement
• Excess Representation Among the given options, Sign-and-Magnitude and 1's Complement are standard methods used to represent signed numbers.

Step 1: Understand Sign-and-Magnitude representation.
In this method:
• Leftmost bit = Sign bit
• Remaining bits = Magnitude Example: \[ +5 = 0101 \] \[ -5 = 1101 \] Hence it represents both positive and negative numbers. \[ (a)=\text{True} \]

Step 2: Understand 1's Complement representation.
Negative numbers are obtained by complementing every bit. Example: \[ +5 = 0101 \] \[ -5 = 1010 \] Therefore it also represents signed numbers. \[ (c)=\text{True} \]

Step 3: Analyze the remaining options.
Sign-9's complement and Sign-10's complement are decimal complement methods and are not standard binary signed-number representation systems in this context. \[ (b)=\text{False} \] \[ (d)=\text{False} \]

Step 4: Identify the correct pair.
\[ (a)\ \text{and}\ (c) \] Therefore, \[ \boxed{(a)\text{ and }(c)} \] Hence option (A) is correct.