Computer Science Number Systems and Binary Arithmetic

Vocabulary and fundamental concepts covering binary, denary, and hexadecimal number system conversions, hexadecimal applications, and binary addition rules.

Binary Representation of Denary 128

The denary number 128 converted to binary is $10000000_2$.

Binary Representation of Denary 250

The denary number 250 converted to binary is $11111010_2$.

Hexadecimal Values for 10 through 15

In hexadecimal notation, denary values 10 through 15 are represented by letters A (10), B (11), C (12), D (13), E (14), and F (15).

Hexadecimal 1A to Denary Conversion

Hexadecimal 1A equals denary 26, calculated as $(1 \times 16) + (10 \times 1) = 16 + 10 = 26$.

Hexadecimal FF to Denary Conversion

Hexadecimal FF equals denary 255, calculated as $(15 \times 16) + (15 \times 1) = 240 + 15 = 255$.

Binary $11110000_2$ to Hexadecimal Conversion

The binary value $11110000_2$ converted to hexadecimal is $\text{F0}_{16}$.

Hexadecimal 3C to Binary Conversion

The hexadecimal number 3C converted to binary is $00111100_2$.

Four Uses of Hexadecimal System

The four uses of the hexadecimal system are Error codes, MAC addresses, IPv6 addresses, and HTML colour codes.

Error Codes

Codes that refer to the memory location of the code and are usually automatically generated by computers.

Media Access Control (MAC) Address

A number which uniquely identifies a device on a network, made up of 48 bits shown as six groups of hexadecimal digits (e.g., 00-1C-B3-4F-25-FF).

Binary Addition Rule for $1 + 1$

The result of $1 + 1$ in binary addition is $10_2$ (write 0, carry 1).

Binary Addition Rule for $1 + 1 + 1$

The result of $1 + 1 + 1$ in binary addition is $11_2$ (write 1, carry 1).

Binary Addition of $00011101_2$ and $01100110_2$

The sum of binary numbers $00011101_2 + 01100110_2$ is equal to $10000011_2$.