Q#1: What is the radix point used in the floating-point notation to represent values with a fractional part?
Answer:
- The radix point in binary acts like the decimal point in decimal numbers, separating the whole number part from the fractional part.
- In floating-point notation, a binary value is divided into three fields: sign bit, exponent field, and mantissa field.
- The position of the radix point is determined by the exponent, allowing representation of fractional values.
Q#2: How does the 2’s complement notation represent negative integers, and what is the significance of the sign bit in this representation?
Answer:
- Negative integers in 2’s complement are represented by starting with all 1s and counting down to the desired negative value.
- The leftmost bit is the sign bit:
- 0 = positive
- 1 = negative
- The remaining bits represent the magnitude of the number.
Q#3: What is the problem of overflow in 2’s complement notation, and how can it be addressed in computer systems?
Answer:
- Overflow occurs when the result of an addition exceeds the maximum value representable with the available bits.
- Solutions include:
- Using longer bit patterns (e.g., 32 bits instead of 16 bits)
- Using alternative units or representations (e.g., kilometers instead of meters)
Q#4: What is the normalized form in floating-point notation, and why is it important in ensuring unique representations for values?
Answer:
- Normalized form requires that the mantissa starts with the leftmost 1 in the binary representation.
- Importance:
- Ensures only one unique representation for each value
- Eliminates multiple representations for the same number
- Guarantees consistency for all nonzero values