Chapter 2: Binary Values and Number Systems (Conversions)

Vocabulary flashcards covering key concepts from Chapter 2: Binary Values and Number Systems (Conversion basics).

Base (radix)

The base is the number of digits in a numbering system and determines the value of digit positions; digits range from 0 to base−1.

Base 2 (Binary)

A numbering system that uses only digits 0 and 1; each position represents a power of two.

Base 10 (Decimal)

The standard numbering system using digits 0–9; each position represents a power of ten.

Subscript indicating base

A small base indicator after a number (e.g., 1012) showing which base the number is written in.

Positional notation

A system where a digit's value depends on its position; value = sum of digit_i × base^i.

Natural numbers

Non-negative integers: 0 and all positive integers.

Negative numbers

Numbers less than zero.

Integers

Whole numbers with no fractional part; includes zero, positives, and negatives.

Rational numbers

Numbers expressible as a ratio of two integers (a/b, b ≠ 0); decimals may terminate or repeat.

Digit

A symbol representing a value in a given base; digits range from 0 to base−1.

Bit

A binary digit; a bit is either 0 or 1.

Byte

A group of eight bits.

Exponent

The power to which the base is raised in a positional value.

Division remainder method

Method to convert decimal to binary by repeatedly dividing by 2 and collecting remainders; read remainders bottom-up.

Chart method (powers of two)

Method to convert decimal to binary using a powers-of-two chart; select largest 2^k ≤ n and set corresponding bit to 1, filling gaps with zeros.

Binary to decimal conversion

Converting a base-2 number to base-10 using positional notation (sum of bit_i × 2^i).

Powers of two relationship to bases

Bases that are powers of two (e.g., 2, 8=2^3, 16=2^4) have straightforward mappings to binary.

Verification by positional notation

You can verify conversions by converting back using positional notation to ensure consistency.