Number Systems and Conversions Quiz

A system using a base (radix) to represent numbers. Each number is composed of digits from 0 to base-1.

A number system with base 10, using digits 0-9.

Numbers used for calculations in computers.

A number system with base 2, using only digits 0 and 1.

Converting from one number system to another.

Representing a number in a different base by summing its weighted digits.

A number system with base 8, using digits 0-7. Used in some computer programming and for simplifying binary.

A number system with base 16, using digits 0-9 and letters A-F. Used in programming and addressing memory.

A method of representing negative and positive integers using a dedicated sign bit (most significant bit) for positive or negative sign and the remaining bits for the numeric value.

The range of integers that can be represented using an N-bit signed-magnitude system.

A method of calculating the difference between two numbers using complements instead of direct subtraction. It simplifies subtraction in computer systems.

A complement of a number in a radix r system, derived by subtracting each digit from (r-1) and adding 1 to the result.

A complement of a number in a radix r system, derived by subtracting each digit from (r-1).

An error in signed-number arithmetic that occurs when the result of an operation exceeds the representable range.

Adding two signed-magnitude numbers with the same sign, you add their magnitudes and keep the same sign.

Adding two signed-magnitude numbers with different signs, you determine the larger magnitude. The sign of the result is the sign of the larger magnitude, and the difference of magnitudes is the result.

A numerical representation used in computers, where each digit is a power of 2. It uses only two digits: "0" and "1".

A number system with the base of 16, used for representing memory addresses, data, and color codes in computers. It uses the digits 0-9 and letters A-F.

A standard for representing floating-point numbers in computers, used for storing and processing numbers like decimals and very large values. It involves a sign bit, exponent, and fraction.

A method of converting decimal numbers into binary codes. Each decimal digit is represented by its binary equivalent using four bits.

A way of representing characters (letters, numbers, symbols) using a unique binary code for each character. This allows computers to process and display text.

In binary arithmetic, this occurs when the sum of two numbers of a specific length results in a number that exceeds the length of the register.

Detecting overflow depends on whether the numbers are considered 'signed' or 'unsigned'. You can identify overflow by checking the carries into and out of the sign bit. If they are different, overflow has occurred.

Binary numbers, like decimal numbers, can have decimal points. Each position to the right of the decimal point represents a negative power of 2.

The decimal value of a binary number is determined by adding up the values of each position. The value of each position is determined by its exponent, which is the power of 2 corresponding to its position.

The binary representation of a real number works the same way as decimal numbers, except that each position in the binary number represents a power of two, not a power of ten.

A standard length register, in a digital computer, is a unit of memory used to store a specific number of bits.

A register is a specialized memory location built into the CPU that stores data values. It can be accessed very quickly.

The IEEE Standard 754 is a widely used standard for representing floating-point numbers in computers. It defines formats for representing numbers with different precisions, including single-precision (32 bits) and double-precision (64 bits).

In the IEEE Standard 754, a floating-point number is represented in three parts: a sign bit, an exponent, and a fraction (or mantissa).

The sign bit determines the sign of the floating-point number. A '0' represents a positive number, and a '1' represents a negative number.

The exponent indicates the power of two that the fraction is multiplied by. It's typically represented in a biased form, where a fixed value is added to the actual exponent.

The fraction (or mantissa) represents the significant digits of the floating-point number. It's often normalized to have a leading '1' to maximize the number of significant digits.

Single-precision floating-point numbers use 32 bits to represent a number. They provide a balance between accuracy and performance.

Double-precision floating-point numbers use 64 bits and offer more precision than single-precision. They can represent larger numbers and with more decimal places.

The IEEE Standard 754 also defines special values to represent infinite, negative infinity, and zero. These values are used in situations where a result might exceed the range of representable numbers.

A method of representing decimal numbers using 4 bits for each digit, ranging from 0000 to 1001. Each digit is represented independently, unlike binary where the entire number is converted.

A set of characters that includes numbers, letters, and special symbols. It is used in computers to represent textual information.

A standard binary code that uses 7 bits to represent 128 characters, including letters, numbers, and special symbols. It is commonly used in computers for text encoding.

An 8-bit code that extends BCD to represent a wider range of characters, including control characters, special characters, and uppercase letters. It is primarily used in mainframe computers.

A 16-bit character encoding standard that supports a vast range of characters from almost every language in the world, making it suitable for universal communication.

The conversion of a decimal number into its binary equivalent, where each digit is represented by a series of 1s and 0s.

The process of representing a decimal number using a specific binary code, such as BCD, where each decimal digit is represented by a specific binary code.