Set Bit (Bit Set)

Set a specific bit in a binary number to 1

Bit Set Calculator

Bit Operation: Set

This function sets (sets to 1) a specific bit in a binary number. The numbering starts with the rightmost bit at position 0.

Example: 80 (hex) = 128 (dec) = 10000000 (binary)
Bit Position (to set)
Position 0: rightmost bit | Position 1: second bit | Position 2: third bit, etc.
Results after Bit-Set Operation
Binary:
Octal:
Decimal:
Hexadecimal:

Bit-Set Visualization

Example: 80 (hex) → Set Bit 2
Original: 1 0 0 0 0 0 0 0
Position: 7 6 5 4 3 2 1 0
After Set Bit 2: 1 0 0 0 0 1 0 0
84 (hex) = 132 (dec)
Bit Set Operation

Target Bit = 1

Other bits remain unchanged

Logical OR operation with mask
Important Properties
  • Bit position starts at 0 (right)
  • Only the specified bit is set to 1
  • Already set 1-bits remain unchanged
  • Operation is idempotent (multiple executions = same effect)

Mathematical Foundations of Bit-Set Operation

The Bit-Set operation uses a logical OR operation with a special mask:

Mask Creation
\[\text{Mask} = 1 \ll n\]

n = bit position, << = left shift

Bit-Set Operation
\[\text{Result} = \text{Original} \Or \text{Mask}\]

Logical OR operation with the generated mask

Bit-Set Formulas and Examples

General Bit-Set Formula
\[\text{set\_bit}(x, n) = x \Or (1 \ll n)\]

Where x is the original number and n is the bit position

Step-by-Step Example: Set Bit 2 in 80 (hex)

1. Original: 10000000₂ (80 hex = 128 dec)

2. Bit Position: n = 2

3. Create Mask: 1 << 2 = 00000100₂

4. OR Operation: 10000000₂ | 00000100₂ = 10000100₂

5. Result: 84 hex = 132 dec

More Examples
Set Bit 0 in 14 (dec):
Original: 1110₂ (14)
Mask: 0001₂
Result: 1110₂ | 0001₂ = 1111₂ (15)
Set Bit 3 in 240 (dec):
Original: 11110000₂ (240)
Mask: 00001000₂
Result: 11111000₂ (248)
OR Operation (|) Truth Table
A
B
A | B
Meaning
0
0
0
Both 0 → 0
0
1
1
One 1 → 1
1
0
1
One 1 → 1
1
1
1
Both 1 → 1

The OR operation sets a bit if it is 1 in the mask

Bit-Set Reference

Standard Example
Original: 80 (hex) Bit 2 set: 84 (hex) Difference: +4 (dec)
Bit Values (Powers of 2)

Bit 0: 2⁰ = 1

Bit 1: 2¹ = 2

Bit 2: 2² = 4

Bit 3: 2³ = 8

Bit 4: 2⁴ = 16

Bit 5: 2⁵ = 32

Bit 6: 2⁶ = 64

Bit 7: 2⁷ = 128

Logical Operators

|: bitwise OR

&: bitwise AND

^: bitwise XOR (exclusive OR)

~: bitwise negation (NOT)

<<: left shift

Common Operations

Set Bit: x | (1 << n)

Clear Bit: x & ~(1 << n)

Toggle Bit: x ^ (1 << n)

Check Bit: (x >> n) & 1

Bit Manipulation - Detailed Description

Bit Set Operation

The bit-set operation is a fundamental bitwise operation that sets a specific bit in a binary number to 1, while leaving all other bits unchanged. This operation is essential for hardware control and systems programming.

Properties:
• Target bit is always set to 1
• Other bits remain unchanged
• Operation is idempotent
• Based on logical OR operation

OR Mask Technique

The OR mask technique is the heart of the bit-set operation. A mask is created that contains a 1 at the desired position and 0s at all other positions. This mask is then OR-combined with the original number.

Mask Creation

1. Create bit pattern: 1 << n
2. OR operation: original | mask
3. Result: Bit n is set

Practical Applications

Bit-set operations are indispensable in hardware programming and system control. They enable targeted activation of features, flags, and control bits without affecting other system states.

Application Areas:
• Activate hardware registers
• Set status flags
• Grant permissions
• Enable feature flags

OR Operation

The logical OR operation is the foundation of the bit-set operation. It returns 1 when at least one of the input bits is 1, thereby setting bits but never clearing them.

OR Properties
  • 0 | 0 = 0 (both bits remain 0)
  • 0 | 1 = 1 (bit is set)
  • 1 | 0 = 1 (bit remains set)
  • 1 | 1 = 1 (bit remains set)

Practical Bit-Set Examples

Hardware Activation

Scenario: Turn on LED

Register: 10100000₂

Set Bit 3: 10101000₂

Effect: LED at position 3 on

Status Flags

Scenario: Set ready flag

Status: 01110000₂

Set Bit 7: 11110000₂

Effect: System ready

Permissions

Scenario: Grant write permission

Rights: 101₂ (r-x)

Set Bit 1: 111₂ (rwx)

Effect: Full access granted

Programming Tips
  • Use constants: #define BIT2 (1<<2)
  • Define macros: #define SET_BIT(x,n) ((x) | (1<<(n)))
  • Use bit fields: for structured data
  • Debugging: Binary output for control
  • Atomic operations: for thread safety
  • Combine bitmasks: multiple bits simultaneously


IT Functions

Decimal, Hex, Bin, Octal conversion • Shift bits left or right • Set a bit • Clear a bit • Bitwise AND • Bitwise OR • Bitwise exclusive OR

Special functions

Airy • Derivative Airy • Bessel-I • Bessel-Ie • Bessel-J • Bessel-Je • Bessel-K • Bessel-Ke • Bessel-Y • Bessel-Ye • Spherical-Bessel-J • Spherical-Bessel-Y • Hankel • Beta • Incomplete Beta • Incomplete Inverse Beta • Binomial Coefficient • Binomial Coefficient Logarithm • Erf • Erfc • Erfi • Erfci • Fibonacci • Fibonacci Tabelle • Gamma • Inverse Gamma • Log Gamma • Digamma • Trigamma • Logit • Sigmoid • Derivative Sigmoid • Softsign • Derivative Softsign • Softmax • Struve • Struve table • Modified Struve • Modified Struve table • Riemann Zeta

Hyperbolic functions

ACosh • ACoth • ACsch • ASech • ASinh • ATanh • Cosh • Coth • Csch • Sech • Sinh • Tanh

Trigonometrische Funktionen

ACos • ACot • ACsc • ASec • ASin • ATan • Cos • Cot • Csc • Sec • Sin • Sinc • Tan • Degree to Radian • Radian to Degree