BINARY

1. Number Systems: Decimal vs. Binary

The foundation of computing relies on understanding the difference between the base-10 system used by humans and the base-2 system used by computers.

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  • Decimal (Base 10): Uses ten digits (0–9). Each position represents a power of 10 (e.g., 100, 101, 102).

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  • Binary (Base 2): Uses two digits (0 and 1). Each position represents a power of 2 (e.g., 20, 21, 22).

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2. Data Units: Bits, Bytes, Nibbles, and Words

Computer architecture organizes data into specific sizes for processing and storage.

  • Bit: A portmanteau of "Binary Digit". It is the smallest unit of information, representing a state of "on" or "off" (or high/low voltage) in a digital circuit.

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  • Byte: Consists of 8 bits. It is the smallest addressable unit of computer storage, meaning it can be retrieved based on its specific location in memory.

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  • Nibble (Nybble): Half of a byte, consisting of 4 bits. A byte contains a "high-order" nibble and a "low-order" nibble.

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  • Word: A contiguous group of two or more adjacent bytes. The "word size" is the best size handled by a specific computer's architecture; common sizes are 16, 32, or 64 bits.

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3. The Metric System in Computing

Metrics are used to measure capacity (storage) and speed.

Prefix

Symbol

Power of 10

Power of 2

Kilo-

K

103 (1 thousand)

210 (1,024)

Mega-

M

106 (1 million)

220

Giga-

G

109 (1 billion)

230

Tera-

T

1012 (1 trillion)

240

Peta-

P

1015 (1 quadrillion)

250

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  • Note: Whether a metric refers to a power of 10 or a power of 2 usually depends on what is being measured. For example, a "1 GB" hard drive often contains exactly 109 bytes rather than the binary 230 bytes.

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4. Binary Prefixes (Kibi vs. Kilo)

To be technically precise, different prefixes exist to distinguish binary powers from decimal powers.

  • Kibibyte (KiB): Derived from "kilobinary," representing exactly 1,024 bytes.

  • Sequential Binary Units: Mebibytes (MiB), Gibibytes (GiB), Tebibytes (TiB), Pebibytes (PiB), and Exbibytes (EiB).

  • Standard Usage: While "kibibyte" is technically correct for data storage, many people still use the decimal term "kilobyte" to refer to binary amounts.

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