Number system conversions are fundamental concepts in computing that involve translating values between different numerical bases. The four primary number systems used in technology are decimal (base-10), binary (base-2), hexadecimal (base-16), and octal (base-8).
Decimal is the standard system hu…Number system conversions are fundamental concepts in computing that involve translating values between different numerical bases. The four primary number systems used in technology are decimal (base-10), binary (base-2), hexadecimal (base-16), and octal (base-8).
Decimal is the standard system humans use daily, utilizing digits 0-9. Binary is the language of computers, using only 0s and 1s to represent data. Each binary digit (bit) represents a power of 2. Hexadecimal uses digits 0-9 and letters A-F, making it convenient for representing large binary numbers in a more compact form. Octal uses digits 0-7 and was historically significant in early computing.
To convert decimal to binary, repeatedly divide the decimal number by 2 and record the remainders. Reading the remainders from bottom to top gives the binary equivalent. For example, decimal 13 becomes binary 1101.
Converting binary to decimal involves multiplying each bit by its corresponding power of 2 and summing the results. Binary 1101 equals (1×8)+(1×4)+(0×2)+(1×1) = 13 in decimal.
Hexadecimal conversions are particularly useful because each hex digit represents exactly four binary digits. To convert binary to hex, group binary digits into sets of four from right to left, then convert each group. Binary 11010110 becomes D6 in hexadecimal.
For decimal to hexadecimal conversion, divide the decimal number by 16 and track remainders, similar to the binary conversion process.
Understanding these conversions is essential for IT professionals because computers process all data in binary, memory addresses are typically displayed in hexadecimal, and network configurations often require working with different number systems. Mastering these conversions helps technicians troubleshoot hardware issues, understand memory allocation, configure network settings, and interpret system-level information effectively.
Number System Conversions - Complete Guide
Why Number System Conversions Are Important
Understanding number system conversions is fundamental to IT and computing. Computers operate using binary (base-2), while humans typically work with decimal (base-10). Hexadecimal (base-16) is commonly used in programming, memory addresses, MAC addresses, and color codes. Being able to convert between these systems is essential for troubleshooting, networking, and understanding how data is stored and processed.
What Are Number Systems?
A number system is a way of representing numerical values using a specific set of digits or symbols.
Binary (Base-2): Uses only 0 and 1. This is the native language of computers.
Decimal (Base-10): Uses digits 0-9. This is our everyday counting system.
Hexadecimal (Base-16): Uses digits 0-9 and letters A-F (where A=10, B=11, C=12, D=13, E=14, F=15). Used to represent large binary numbers in a compact form.
Octal (Base-8): Uses digits 0-7. Less common but sometimes appears in computing contexts.
How Number Conversions Work
Binary to Decimal: Multiply each binary digit by 2 raised to its position power (starting from 0 on the right), then add all results. Example: 1101 = (1×8) + (1×4) + (0×2) + (1×1) = 13
Decimal to Binary: Divide the decimal number by 2 repeatedly, recording remainders. Read remainders from bottom to top. Example: 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1 → 1101
Binary to Hexadecimal: Group binary digits into sets of 4 (from right to left), then convert each group to its hex equivalent. Example: 11010110 → 1101 0110 → D6
Hexadecimal to Binary: Convert each hex digit to its 4-bit binary equivalent. Example: 2F → 0010 1111
Hexadecimal to Decimal: Multiply each hex digit by 16 raised to its position power, then add. Example: 2F = (2×16) + (15×1) = 47
Exam Tips: Answering Questions on Number System Conversions
1. Memorize key binary values: Know powers of 2 (1, 2, 4, 8, 16, 32, 64, 128, 256) by heart.