Binary and Two's Complement Quiz

<p>It has a unique representation. (A)</p> Signup and view all the answers

<p>-(2^{n -1}) ≤ N ≤ +(2^{n -1} - 1) (B)</p> Signup and view all the answers

<p>0011 (D)</p> Signup and view all the answers

<p>Adjust the exponents to be equal. (D)</p> Signup and view all the answers

<p>-3 to +3 (C)</p> Signup and view all the answers

<p>Raise to the largest exponent and normalize the result. (D)</p> Signup and view all the answers

<p>a + 2^n = a modulo 2^n (C)</p> Signup and view all the answers

<p>10111011 (A)</p> Signup and view all the answers

<p>The sign of the number (D)</p> Signup and view all the answers

<p>a - b = a + (-b) (B)</p> Signup and view all the answers

<p>1's complement of N plus 1 (D)</p> Signup and view all the answers

<p>N (C)</p> Signup and view all the answers

<p>a + 2's C(b) (C)</p> Signup and view all the answers

<p>1010 (C)</p> Signup and view all the answers

<p>0010 (B)</p> Signup and view all the answers

<p>One bit (C)</p> Signup and view all the answers

<p>256 (D)</p> Signup and view all the answers

<p>01000001 (C)</p> Signup and view all the answers

<p>Indicate the sign of the number (C)</p> Signup and view all the answers

<p>It requires more complex circuits for arithmetic operations (C)</p> Signup and view all the answers

<p>Two (B)</p> Signup and view all the answers

<p>$-(2^{(n-1)} - 1) ext{ to } +(2^{(n-1)} - 1)$ (B)</p> Signup and view all the answers

<p>Sign/absolute value, 1's complement, and 2's complement (D)</p> Signup and view all the answers

<p>It is simple and straightforward to understand (A)</p> Signup and view all the answers

<p>Ambiguity leading to errors in arithmetic operations (B)</p> Signup and view all the answers

<p>-3 to +3 (A)</p> Signup and view all the answers

<p>11 (D)</p> Signup and view all the answers

<p>The leading 1 in the mantissa (A)</p> Signup and view all the answers

<p>127 (C)</p> Signup and view all the answers

<p>By subtracting the bias from the biased exponent (B)</p> Signup and view all the answers

<p>Each digit is represented as a 4-bit binary value (C)</p> Signup and view all the answers

<p>The same as calculated without biased exponent (C)</p> Signup and view all the answers

<p>1 bit for sign, 11 bits for exponent, 52 bits for mantissa (D)</p> Signup and view all the answers

A method of representing negative numbers where the most significant bit (MSB) indicates the sign (0 for positive, 1 for negative) and the remaining bits represent the absolute value of the number.

A bit pattern used to represent a number, where each bit represents a power of 2.

An operation that changes the value of a bit by inverting its state (0 becomes 1, 1 becomes 0).

A method for representing negative numbers where the negative number is found by inverting all the bits of the positive number and adding 1.

The maximum value that can be represented using a specific number of bits.

The minimum value that can be represented using a specific number of bits. Often a negative value in two's complement.

The process of representing a value in a different numbering system, such as converting from decimal to binary.

Representing real numbers (numbers with fractional parts) in a computer's memory. Common techniques involve using fixed-point or floating-point representations.

The most significant bit (MSB) in a Two's Complement representation indicates the sign of the number. If the MSB is 1, the number is negative. If it is 0, the number is positive.

The Two's Complement representation allows us to perform arithmetic operations (addition and subtraction) using a single set of rules, regardless of whether the numbers are positive or negative. This simplifies the process of operations in computers.

On n bits, the range of values that can be represented in Two's Complement is from -2^(n-1) to +(2^(n-1) - 1). This means that for n=3 bits, the possible values range from -4 to +3.

Zero (0) in Two's Complement is represented by all bits being set to 0. It has a unique representation and does not have a double representation.

A machine representation for real numbers using a fixed-point format, consisting of a sign bit, a biased exponent, and a normalized mantissa.

The process of converting a real number into its floating-point representation by adjusting the exponent and mantissa to ensure the number is properly normalized.

The value added to the true exponent to obtain a positive biased exponent, allowing for efficient representation within the allotted bits.

The addition of two floating point numbers that have the same exponent by directly adding their mantissas.

The addition of two floating point numbers with different exponents by adjusting the smaller exponent to match the larger exponent and then adding the mantissas.

The range of values representable on 'n' bits using 1's complement representation. It spans from -(2^(n-1)-1) to +(2^(n-1)-1).

A mathematical concept ensuring that adding 2^n to a number 'a' represented in binary form on 'n' bits, and then taking the result on those 'n' bits, returns the original value 'a'.

A method to represent negative numbers in binary. It involves inverting all bits of the positive equivalent and adding 1.

The process of finding the 2's complement of a number. It involves inverting all bits starting from the least significant bit until the first '1' and then keeping all bits before that '1'.

The most significant bit (MSB) in a 2's complement representation determines the sign of the number. A '0' MSB indicates a positive number, while a '1' MSB indicates a negative number.

The 2's complement of the 2's complement of a number 'N' results in the original number 'N'. This property is crucial for performing arithmetic operations.

The process of converting a subtraction operation into an addition operation in 2's complement representation. It involves adding the 2's complement of the subtrahend to the minuend.

The decimal value of a binary number in 2's complement form is determined by considering the sign bit. If the sign bit is '1' (negative), the value is calculated by taking the 2's complement of the binary representation and then negating it.

A numerical value that determines the shift applied to the exponent part of a floating-point number.

The exponent representation of a floating-point number after applying the bias, helping to handle both positive and negative exponents.

A standardized representation for floating point numbers, defining two formats: 32-bit single precision and 64-bit double precision.

The fractional part of a floating-point number, normalized to a range between 1 and 2, with the leading 1 bit often implicit.

The leading 1 in the mantissa of a floating-point number that's not explicitly stored in the computer, to save space.

A method of representing numbers using 4 bits per decimal digit, where each digit is converted to its corresponding binary equivalent.

The representation of numbers with fractional parts, using various methods such as fixed-point or floating-point, to handle both integer and fractional parts.

A system where each digit 0-9 is represented by a 4-bit BCD code, but with 3 added to each value. This allows for a more compact representation of numbers using binary.

A binary code where consecutive values differ by only one bit. This eliminates the issue of multiple-bit changes leading to errors.

A standard for representing characters using 8-bit code combinations, allowing for 256 unique characters.

A 16-bit encoding scheme that supports a wider range of characters than ASCII, accommodating diverse languages and symbols.

A system where combinations greater than 9 are not used for representing numbers, ensuring a consistent 4-bit representation within the system.