Data Representation: Binary vs Decimal Prefixes

Study Notes

Data Representation

Binary magnitudes refer to the way data storage and transmission capacities are measured using binary prefixes.
Binary prefixes are based on powers of 2, whereas decimal prefixes are based on powers of 10.

Binary and Decimal Prefixes

Kibi (Ki) = 2^10, Kilobyte (KB) = 10^3
Mebi (Mi) = 2^20, Megabyte (MB) = 10^6
Gibi (Gi) = 2^30, Gigabyte (GB) = 10^9
Tebi (Ti) = 2^40, Terabyte (TB) = 10^12

Number Systems

Binary (base-2): Uses digits 0 and 1, where each digit represents a power of 2.
Denary (decimal, base-10): Uses digits 0 to 9, where each digit represents a power of 10.
Hexadecimal (base-16): Uses digits 0 to 9 and letters A to F (representing 10 to 15), where each digit represents a power of 16.

Binary Coded Decimal (BCD)

Represents each decimal digit with a 4-bit binary number.
Example: The decimal number 25 is represented as 0010 0101 in BCD.

One's and Two's Complement Representation

One's complement is formed by flipping all the bits of a binary number.
Example: The one's complement of 1010 is 0101.
Two's complement is formed by adding 1 to the one's complement.
Two's complement is used to represent negative numbers in binary.
Example: The two's complement of 1010 is 1010 + 1 = 1011.

Converting Between Number Bases

From Denary to Binary:
- Divide the denary number by 2 and note down the remainder (0 or 1) each time.
- The binary equivalent is the sequence of remainders read from bottom to top.
From Denary to Hexadecimal:
- Divide the denary number by 16 and note down the remainder (0 to F) each time.
- The hexadecimal equivalent is the sequence of remainders read from bottom to top.
From Binary to Denary:
- Multiply each binary digit (from right to left) by 2 raised to the corresponding power of 2 (starting from 0).
- Sum up these values to get the denary equivalent.
From Binary to Hexadecimal:
- Group the binary number into sets of 4 bits (starting from the right) and convert each group to its hexadecimal equivalent.
From Hexadecimal to Denary:
- Multiply each hexadecimal digit (from right to left) by 16 raised to the corresponding power of 16 (starting from 0).
- Sum up these values to get the denary equivalent.
From Hexadecimal to Binary:
- Convert each hexadecimal digit to its 4-bit binary equivalent.

Binary Arithmetic

Binary Addition:
- Start from the rightmost bit (least significant bit) and move left.
- Add the corresponding bits from each number along with the carry (if any) from the previous addition.
- If the sum is 0 or 1, write it down and carry 0.
- If the sum is 2, write down 0 and carry 1.
- If the sum is 3, write down 1 and carry 1.
Binary Subtraction:
- Find the two's complement of the number to be subtracted (invert all bits and add 1).
- Add this two's complement to the other number (the minuend).
- If there is a carry out of the most significant bit, overflow occurs.

Description

This quiz explains the difference between binary prefixes (kibi, mebi, gibi, tebi) and decimal prefixes (kilo, mega, giga, tera) in the context of data representation. It covers how these prefixes are related to binary magnitudes and how they are used to measure data storage and transmission capacities.