Computer Number Systems

This set of vocabulary flashcards covers the definitions, characteristics, and conversion principles of computer number systems including Positional, Non-positional, Decimal, Binary, Octal, and Hexadecimal systems.

Number System

A mathematical notation for representing quantities using a consistent set of symbols (digits) and rules.

Positional system

A system where the value of each digit depends on BOTH the digit AND its position (place) within the number.

Non-positional system

A system where each symbol has a fixed absolute value regardless of where it appears, requiring the sum of all values to find the total.

Base (Radix)

The number of unique digits in a system, which determines positional weights (powers of the base).

Bit

A single binary digit ($0$ or $1$) that serves as the fundamental unit of storage in all digital computers.

Roman Numeral Expansion Rule

The total value is found by adding symbol values left to right; however, if a smaller value appears immediately before a larger value, the smaller is subtracted from the larger (subtractive notation).

Positional Number System Formula

$\text{Value} = d_n \times r^n + d_{n-1} \times r^{n-1} + \dots + d_1 \times r^1 + d_0 \times r^0$ where $r$ is the base and $d$ is the digit.

Decimal Number System

A base $10$ system using digits $0$-$9$; it serves as the reference point for human base conversions.

Binary Number System

A base $2$ system using digits $0$ and $1$ that corresponds to digital voltage states (high/$1$ and low/$0$).

Byte

A data unit consisting of $8$ bits, which can represent a maximum decimal value of $255$.

Octal Number System

A base $8$ system using digits $0$-$7$ where each digit maps exactly to $3$ binary bits.

Hexadecimal Number System

A base $16$ system using digits $0$-$9$ and letters $A$-$F$ ($A=10$, $B=11$, $C=12$, $D=13$, $E=14$, $F=15$).

Nibble

A unit of data consisting of $4$ binary bits, equivalent to exactly one hexadecimal digit.

Successive division by 2

The method used for converting decimal integers to binary by recording remainders and reading them from bottom to top.

Successive multiplication by 2

The method used for converting decimal fractions to binary by recording integer carries and reading them from top to bottom.

Binary to Hex shortcut

The process of grouping binary bits in fours from the right and replacing each group with its corresponding hexadecimal digit.

Binary to Octal shortcut

The process of grouping binary bits in threes from the right and replacing each group with its corresponding octal digit.