Chapter 5 Terms and Definitions

Sign-and-Magnitude

"0" indicates a positive integer, and "1" indicates a negative integer. The rest of the bits are used for the magnitude of the number. So -2410 is represented as: 1001 1000 The sign "1" means negative The magnitude is 24 (in 7-bit binary)

Wraparound

A facility by which a linear sequence of memory locations or screen positions is treated as a continuous circular series.

Complement

A number or quantity of something required to make a group complete. The opposite/complement value of a particular numeral, commonly found when dealing with a positive and negative number in an arithmetic addition. You'll likely need to find the complement of a negative to add to the positive, as a computer would be able to more appropriately represent the calculation in this manner, and likely may not hold a fixed value as ranges can be limited.

Exponent

A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression (e.g., 3 in 23 = 2 × 2 × 2).

Binary-Coded Decimal (BCD)

A system for coding a number in which each digit of a decimal number is represented individually by its binary equivalent. A number represented as a binary coded decimal.

Exponential notation

Exponential notation is a mathematical method for writing longer multiplication problems in a simplified manner. This lesson will define how to work with exponential notation and give some examples of how it is used.

End-Round-Carry

If a carry is generated at the most significant end of the two numbers, then this carry must be added to the digit at the least significant end of the result to give the radix-minus-one complement representation of the sum. end-around-carry.

Carry Flag

In computer processors the carry flag (usually indicated as the C flag) is a single bit in a system status (flag) register used to indicate when an arithmetic carry or borrow has been generated out of the most significant ALU bit position.

Normalization

Normalization is typically a refinement process after the initial exercise of identifying the data objects that should be in the database, identifying their relationships, and defining the tables required and the columns within each table.

2's Complement

Positive 2's complement numbers are represented as the simple binary. Negative Numbers. Negative 2's complement numbers are represented as the binary number that when added to a positive number of the same magnitude equals zero.

Floating point numbers

Real Numbers: pi = 3.14159265... e = 2.71828... Scientific Notation: has a single digit to the left of the decimal point. A number in Scientific Notation with no leading 0s is called a Normalized Number: 1.0 × 10-8.

Single-Precision Floating Point Format

Single-precision floating-point format is a computer number format that occupies 4 bytes (32 bits) in computer memory and represents a wide dynamic range of values by using a floating point. In IEEE 754-2008 the 32-bit base 2 format is officially referred to as binary32. It was called single in IEEE 754-1985.

Floating point format

Single-precision floating-point format is a computer number format that occupies 4 bytes (32 bits) in computer memory and represents a wide dynamic range of values by using a floating point. In IEEE 754-2008 the 32-bit base 2 format is officially referred to as binary32. It was called single in IEEE 754-1985.

Overflow

The generation of a number or some other data item that is too large for an assigned location or memory space.

Underflow

The generation of a number that is too small to be represented in the device meant to store it.

1's Complement

The ones' complement of a binary number is defined as the value obtained by inverting all the bits in the binary representation of the number (swapping 0s for 1s and vice versa).

Signed Integers

The only guaranteed difference between a signed and an unsigned value in C is that the signed value can be negative, 0 or positive, while an unsigned can only be 0 or positive. The problem is that C doesn't define the format of types (so you don't know that your integers are in two's complement).

Mantissa

The part of a floating-point number that represents the significant digits of that number, and that is multiplied by the base raised to the exponent to give the actual value of the number.

Inversion

The process of finding a quantity, function, etc., from a given one such that the product of the two under a particular operation is the identity. The interchanging of numerator and denominator of a fraction, or antecedent and consequent of a ratio. The process of finding the expression that gives a given expression under a given transformation.

Real Numbers

The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356..., the square root of two, an irrational algebraic number) and π (3.14159265..., a transcendental number).