Number System Columns — TechKnowSurge

About this interactive

Decimal, binary and hexadecimal are the same idea with a different base. A base-10 system has ten digits, 0 to 9; base 2 has two, 0 and 1; base 16 has sixteen. Zero is always the first digit, so the largest digit is one less than the base. Each column is worth the base times the column to its right: decimal 1, 10, 100, 1,000; binary 1, 2, 4, 8, 16; hexadecimal 1, 16, 256, 4,096, 65,536. A digit is worth its value times its column, so the 4 in 148 is 4 x 10 = 40. Counting adds one each time. When a column passes its largest digit, it resets to 0 and carries 1 into the next column, like an odometer: 9 then 10 in decimal, 1 then 10 in binary. A clock does the same with seconds at 59 and hours at 23. Type each answer as digits. Where a question asks what digits are worth, answer in decimal. Commas are optional.

What you'll learn

Compare decimal, binary and hexadecimal by how they work: how many digits each base uses, what each column is worth, and where counting resets and carries

Aligned to

CompTIA Tech+

1.1 Compare and contrast notational systems.

Key terms

Decimal: The base-10 number system using digits 0–9; the standard system used in everyday counting and arithmetic, and the most common format for presenting numeric output to humans.
Binary: The base-2 number system that uses only the digits 0 and 1; the native language of digital computers, which store and process data as electrical on/off states.
Hexadecimal: A base-16 number system using digits 0–9 and letters A–F; each hex digit maps to exactly 4 bits, making it a compact shorthand for representing binary data.
Place Value: The weight assigned to a digit based on its position within a number; in binary, each position represents a successive power of 2 (1, 2, 4, 8, …), making position the key to decoding binary values.
Base Notation: A way of describing a number system by the count of unique digits it uses, such as base-2 for binary or base-10 for decimal.

Topics

Number Systems Binary Decimal Hexadecimal Interactive Calculation

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