Number-Systems & Complements Vocabulary

Key vocabulary covering binary, octal, hexadecimal systems, one’s and two’s complement representations, and related arithmetic concepts.

Unsigned Binary Number

A binary representation that treats every bit as part of the magnitude; all values are non-negative and range from 0 to 2ⁿ−1 for an n-bit word.

Signed Bit (MSB)

In signed representations, the most-significant bit indicates the sign: 0 = positive, 1 = negative.

One’s Complement Representation

A signed number system in which negative values are produced by inverting every bit of the positive value; it has two different encodings of zero (+0 and −0).

Two’s Complement Representation

A signed number system where a negative number is formed by taking the one’s complement of the magnitude and adding 1; provides a single zero and simplifies arithmetic.

Hexadecimal (Hex) Number System

Base-16 numeral system using digits 0–9 and letters A–F, where each hex digit represents four binary bits.

Octal Number System

Base-8 numeral system using digits 0–7, where each octal digit maps to exactly three binary bits.

Binary-to-Decimal Conversion

Process of multiplying each binary digit by its positional power of two and summing the results to obtain a base-10 value.

Decimal-to-Binary Conversion (Division-by-2 Method)

Repeatedly divide the decimal number by 2, recording remainders; the binary number is the remainders read in reverse order.

Two’s Complement Subtraction

Subtracting B from A by adding A to the two’s complement of B; any final carry-out is discarded.

Overflow (Two’s Complement)

An error occurring when the result of an addition/subtraction exceeds the representable range; detected when carries into and out of the sign bit differ.

Bit

The smallest unit of digital information, taking a value of 0 or 1.

Nibble

A grouping of four bits; exactly one hexadecimal digit.

Byte

A grouping of eight bits; commonly used as the basic addressable unit of memory.

MSB (Most Significant Bit)

The highest-weighted bit position in a binary number; often used as the sign bit in signed representations.

LSB (Least Significant Bit)

The lowest-weighted bit position in a binary number; represents 2⁰.