study_flashcards_with_answers
What are unsigned integers?
Unsigned integers are positive whole numbers without a sign bit.
How is a decimal integer converted to binary?
A decimal integer is converted to binary by expressing it in powers of 2.
What is the value range for 4-bit BCD vs binary?
4-bit BCD can represent values from 0 to 9, while 4-bit binary can represent values from 0 to 15.
Why is binary representation preferred over BCD?
Binary representation is preferred because it allows a greater range of values for a given number of bits and simplifies calculations.
In which applications is BCD preferred?
BCD is preferred in business applications due to its maintenance of decimal rounding and precision.
What is packed decimal format used for?
Packed decimal format is used to represent real numbers, especially in business and financial applications, like dollars and cents.
What are the different methods for signed-integer representation?
The different methods for signed-integer representation include sign-and-magnitude, 1’s complement, and 2’s complement.
How does sign-and-magnitude representation work?
In sign-and-magnitude representation, the leftmost bit indicates the sign (0 for positive and 1 for negative), while the rest of the bits represent the magnitude.
What are the advantages and disadvantages of sign-and-magnitude representation?
Sign-and-magnitude representation has simpler conceptual understanding but requires complex algorithms for arithmetic operations.
What is the 9’s complement in decimal notation?
The 9’s complement is found by subtracting each digit of a number from 9.
How is the 9’s complement of a number calculated?
To calculate the 9’s complement, subtract the number from a base value made of 9’s (e.g., 999 for 3-digit numbers).
What is the 1’s complement in binary notation?
The 1’s complement in binary is obtained by inverting all the bits (changing 1’s to 0’s and vice versa).
How is the 1’s complement of a binary number found?
Invert each bit in the binary number to find the 1’s complement.
What are the properties of complementary representation?
Complementary representation does not need separate handling of the sign, making arithmetic consistent for positive and negative numbers.
Explain modular addition with 9’s complement.
Modular addition with 9’s complement involves adding numbers and adjusting by adding a carry if the result overflows the modulus.
What is end-around carry and when is it used?
End-around carry is used in modular arithmetic when the result has more digits than specified; the excess is added back to the result.
What is overflow in binary arithmetic?
Overflow occurs when an arithmetic operation results in a number that exceeds the range allowed by the fixed number of bits.
How is overflow detected in binary addition?
Overflow is detected if both inputs have the same sign but the result has a different sign.
What are the two’s complement properties and usage?
Two’s complement uses the highest bit as the sign and supports straightforward arithmetic operations. It can be found by inverting all bits and adding 1.
How do you find the two’s complement of an 8-bit number?
To find the two’s complement, invert the bits and add 1 to the least significant bit.
What is the role of a carry flag in arithmetic operations?
The carry flag indicates when an operation produces a carry out of the most significant bit, signaling overflow.
How do you perform floating-point addition and subtraction?
For floating-point addition, the exponents must be aligned, and the mantissas are then added or subtracted.
What is normalization in floating-point arithmetic?
Normalization ensures the decimal point is in the correct position, maintaining the format’s precision.
Describe the IEEE 754 standard for 32-bit floating-point representation.
The IEEE 754 standard defines 32-bit floating-point representation with 1 sign bit, 8 exponent bits, and 23 mantissa bits.
How do you convert a base-10 number to binary floating-point format?
Convert the whole and fractional parts separately to binary and combine them into floating-point format.
What is excess-N notation in floating-point representation?
Excess-N notation uses a middle value as an offset for representing exponents.
What are the main differences between integer and real number computations?
Integer computations are simpler and faster than real number computations, but real numbers allow for fractional values and a wider range of magnitudes.
Why might a program use packed decimal format in business applications?
Packed decimal format is used in business applications to maintain decimal precision in financial calculations.
How do you detect overflow when adding two positive binary numbers?
Overflow in binary addition occurs if adding two positive numbers results in a negative number.
What is the significance of the exponent in floating-point numbers?
The exponent indicates the power of the base and scales the mantissa in floating-point numbers.
Explain the process of rounding in floating-point multiplication.
Rounding in floating-point multiplication adjusts the result to fit within the available precision.
