Hex Calculator Formula Guide

The Hex Calculator helps you perform arithmetic and logical operations directly in hexadecimal (base-16). It is useful for programmers, electronics engineers, and computer science students who often deal with low-level data or binary systems.

1. Arithmetic Operations in Hex

The rules are the same as in decimal, but values are expressed in base-16 (digits 0–9 and A–F).

• Addition:

   

  $$A + B = C$$ 

  Example:

  $1A3F + FF = 1B3E$ 

• Subtraction:

   

  $$A – B = C$$ 

  Example:

  $1A3F – FF = 1940$ 

• Multiplication:

   

  $$A \times B = C$$ 

  Example:

  $2A \times F = 26A$ 

• Division (shows quotient and remainder):

   

  $$A \div B = Q \, \text{(quotient)}, \, R \, \text{(remainder)}$$ 

  Example:

  $1A3F \div 10 = 1A3 \, \text{remainder} \, F$ 

2. Base Conversions

The calculator can instantly convert between:

• Hex ⇄ Decimal

• Hex ⇄ Binary

• Hex ⇄ Octal

Example:

$$7B_{16}={123}_{10}={1111011}_2={173}_8$$

3. Bitwise Operations

Bitwise functions work at the binary level:

• AND: keeps bit = 1 only if both are 1

• OR: keeps bit = 1 if either is 1

• XOR: keeps bit = 1 if different

• NOT: flips all bits

• SHL / SHR: shift bits left or right

Example:

$$F0F0 \, AND \, 0F0F = 0000$$

F0F0 AND 0F0F=0000

$$F0F0 \, OR \, 0F0F = FFFF$$

F0F0 OR 0F0F=FFFF