Two's Complement Calculator
Convert between decimal and binary using two's complement representation for signed numbers
Two's Complement Converter
Range: -128 to 127
Signed integer representation
Only 0 and 1 digits allowed
Example Calculations
Positive Number: 16
Binary: 16 = 10000
8-bit representation: 00010000
Sign bit (MSB): 0 (positive)
Negative Number: -16
1. Start with 16: 00010000
2. Flip bits: 11101111
3. Add 1: 11110000
Result: 11110000 = -16
Two's Complement Process
Convert to Binary
Convert the absolute value to binary
Invert Bits
Flip all bits (0→1, 1→0)
Add One
Add 1 to get final two's complement
Word Size Ranges
Bits | Min | Max |
---|---|---|
4 | -8 | 7 |
8 | -128 | 127 |
16 | -32,768 | 32,767 |
32 | -2,147,483,648 | 2,147,483,647 |
Key Properties
MSB determines sign: 0 = positive, 1 = negative
Unique representation: Each number has exactly one representation
Arithmetic friendly: Addition and subtraction work normally
Asymmetric range: One more negative than positive number
Understanding Two's Complement
What is Two's Complement?
Two's complement is a binary representation system for signed integers where negative numbers are represented by inverting all bits of the positive number and adding 1. This method allows for efficient arithmetic operations and is widely used in computer systems.
Why Use Two's Complement?
- •Unique representation for each number
- •Arithmetic operations work normally
- •No separate circuitry needed for subtraction
- •Widely supported in hardware
Converting Methods
Binary to Decimal (Method 1)
Treat MSB as negative weight:
1011 = -1×2³ + 0×2² + 1×2¹ + 1×2⁰ = -8 + 0 + 2 + 1 = -5
Binary to Decimal (Method 2)
For negative numbers (MSB = 1):
- 1. Invert all bits
- 2. Add 1
- 3. Convert to decimal
- 4. Apply negative sign