10 - Flashcards_for_Signed_Numbers
What is a fixed-length binary number?
A binary number with a predetermined number of bits.
Why is fixed-length representation important?
Memory addresses have fixed-length locations, making efficient use of storage.
What are the three fixed-length representations for signed numbers?
Signed Magnitude (SM), One’s Complement, and Two’s Complement.
Which signed number representation is used in modern computers?
Two’s Complement.
In Signed Magnitude representation, what does the most significant bit (MSb) indicate?
0 for positive numbers, 1 for negative numbers.
Describe the steps to convert a base-10 number to signed magnitude binary.
- Convert absolute value to binary, 2. Store in n-1 bits, 3. Add sign bit.
What is the main drawback of signed magnitude representation?
It has two representations for zero, making arithmetic operations more complex.
How is One’s Complement representation different from Signed Magnitude?
Negative numbers are represented by bitwise negation of their positive counterpart.
Describe the steps to convert a base-10 number to One’s Complement binary.
- Convert absolute value to binary, 2. Add leading zeros if necessary, 3. If negative, negate each bit.
What is the main disadvantage of One’s Complement representation?
There are two representations for zero, requiring extra logic for arithmetic operations.
How is Two’s Complement representation different from One’s Complement?
Negative numbers are represented by taking One’s Complement and adding 1.
Describe the steps to convert a base-10 number to Two’s Complement binary.
- Convert absolute value to binary, 2. Add leading zeros, 3. If negative, negate each bit and add 1.
What is the range of an 8-bit Two’s Complement number?
-128 to +127.
Why is Two’s Complement preferred in modern computing?
It simplifies arithmetic operations and has only one representation for zero.
What is signed overflow in Two’s Complement representation?
When the result of an operation exceeds the representable range for a given bit-length.
What is the condition for detecting signed overflow in Two’s Complement?
Overflow occurs when adding two positive numbers gives a negative result, or two negative numbers give a positive result.
What is the purpose of the sign bit in signed number representations?
To indicate whether a number is positive or negative.
What is the general formula for the range of an n-bit Two’s Complement number?
-(2^(n-1)) to (2^(n-1) - 1).
How is subtraction handled in Two’s Complement arithmetic?
By adding the negation of the second operand using Two’s Complement rules.
