# Chapter 2 (Binary)

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Binary

Base 2 positional numbering system. Uses the digits 0 and 1.

Found in lecture Chapter 2 - Bits 1 and zyBook Section 2.2

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Bit

Binary Digit

Found in lecture Chapter 2 - Bits 1 and zyBook Section 2.1

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Byte

Group of 8 bits

Found in lecture Chapter 2 - Bits 1 and zyBook Section 2.1

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Overflow

Occurs when computer tries to represent a number that exceeds the maximum value

Found in lecture Chapter 2 - Bits 1 and zyBook Section 2.2

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Binary Numbers

Used to store data internally for numerical values, letters, graphics, etc.

Found in lecture Chapter 2 - Bits 1 and zyBook Section 2.2

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Two's Complement

Leftmost bit represents negative of its positional value

• To find 2's complement, flip the bits and add 1.

Found in lecture Chapter 2 - Bits 2 and zyBook Section 2.3

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Decimal

Base 10 positional numbering system (because humans have 10 fingers)

Found in lecture Chapter 2 - Bits 1 and zyBook Section 2.2

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Base 16 positional numbering system (4 bits = 1 hex digit)

9 9 10 A 11 B 12 C 13 D 14 E 15 F

Found in lecture Chapter 2 - Bits 1 and zyBook Section 2.4

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Code Mapping

Assign each letter or symbol a unique number. Used to represent text in binary. Example: ASCII

Found in lecture Chapter 2 - Bits 4

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ASCII

American standard code mapping for information interchange (widely used 8 bit code mapping)

Found in lecture Chapter 2 - Bits 4 and zyBook Section 2.1

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Unicode

16 and 32 bit code mapping to represent text (used for characters outside of English)

Found in lecture Chapter 2 - Bits 4 and zyBook Section 2.2

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Digitizing

Converts an analog signal (like sound) to a digital number

Found in lecture Chapter 2 - Bits 4 and zyBook Section 2.12

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Sampling

At fixed time intervals, the signal amplitude is measured and stored

Found in lecture Chapter 2 - Bits 4 and zyBook Section 2.12

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Sampling rate

Number of times per second that we measure signal amplitude. For example a sample rate or sampling rate of 44.1 kHz means 44, 100 samples are collected in 1 second.

Found in lecture Chapter 2 - Bits 4 and zyBook Section 2.12

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bit depth

Number of bits used to store each sample. Recall that 16 bit video games can represent more colors than retro-8-bit games because 16 bits can contain 256 times more numerical values then 8 bits.

Found in lecture Chapter 2 - Bits 4 and zyBook Section 2.12

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Pixel

picture element

Found in lecture Chapter 2 - Bits 4 and zyBook Section 2.11

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RGB

The most common format for storing color images. Each pixel has (Red, Green, Blue)

Found in lecture Chapter 2 - Bits 4 and zyBook Section 2.11

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Frame rate

Number of frames (images) shown per second of video.

Found in lecture Chapter 2 - Bits 4 and zyBook Section 2.11

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Pixel bit depth

Number of bits used to store each RGB color (usually at least 8)

Found in lecture Chapter 2 - Bits 4 and zyBook Section 2.11

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number of unique digits, including the digit zero, used to represent numbers in a positional numeral system.

Binary - 2, Octal - 8, Decimal - 10, Hexadecimal - 16, etc.

Found in lecture Chapter 2 - Bits 1 and zyBook Section 2.5/2.6

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Underflow

Occurs when computer tries to represent a number that is less than the minimum value that the device is capable of storing.

Found in lecture Chapter 2 - Bits 4

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floating-point number

A floating-point number is a real number, like 98.6, 0.0001, or -666.667. The term "floating-point" refers to the decimal point being able to appear anywhere ("float") in the number.

Found in lecture Chapter 2 - Bits 3 and zyBook Section 2.6

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normalized scientific notation

floating-point numbers are commonly written using normalized scientific notation, such as 9.86 × 10^1, 1.0 × 10^-4, or -6.66667 × 10^2, where the number is written as a digit (+/- 1 to 9), decimal point, fractional part, times 10 to a power. The term "normalized" is in contrast to non-normalized where more than one digit, or a 0, may precede the decimal point, such as -66.6667 × 10^-0.1 or 0.1 × 10^-3.

Found in lecture Chapter 2 - Bits 3 and zyBook Section 2.6

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significand / mantissa

the part before × in normalized scientific notation

Found in lecture Chapter 2 - Bits 3 and zyBook Section 2.6

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binary point

for binary floating-point numbers, the "dot" is called a binary point (versus decimal point for decimal numbers) The general term is radix point.

Found in lecture Chapter 2 - Bits 3 and zyBook Section 2.6

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analog

a signal that changes continuously over time

Found in lecture Chapter 2 - Bits 4 and zyBook Section 2.12

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digital

a series of binary numbers

Found in lecture Chapter 2 - Bits 4 and zyBook Section 2.12

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