Instantly convert any decimal number into 8-bit binary code with this complete reference and guide.
Understand binary encoding with real examples, formulas, and a full decimal-to-binary conversion chart.
Conversor Decimal a Binario de 8 bits
Extensive Table of Common Decimal to 8-bit Binary Conversions
| Decimal Number | 8-bit Binary Code | Decimal Number | 8-bit Binary Code | Decimal Number | 8-bit Binary Code |
|---|---|---|---|---|---|
| 0 | 00000000 | 43 | 00101011 | 86 | 01010110 |
| 1 | 00000001 | 44 | 00101100 | 87 | 01010111 |
| 2 | 00000010 | 45 | 00101101 | 88 | 01011000 |
| 3 | 00000011 | 46 | 00101110 | 89 | 01011001 |
| 4 | 00000100 | 47 | 00101111 | 90 | 01011010 |
| 5 | 00000101 | 48 | 00110000 | 91 | 01011011 |
| 6 | 00000110 | 49 | 00110001 | 92 | 01011100 |
| 7 | 00000111 | 50 | 00110010 | 93 | 01011101 |
| 8 | 00001000 | 51 | 00110011 | 94 | 01011110 |
| 9 | 00001001 | 52 | 00110100 | 95 | 01011111 |
| 10 | 00001010 | 53 | 00110101 | 96 | 01100000 |
| 11 | 00001011 | 54 | 00110110 | 97 | 01100001 |
| 12 | 00001100 | 55 | 00110111 | 98 | 01100010 |
| 13 | 00001101 | 56 | 00111000 | 99 | 01100011 |
| 14 | 00001110 | 57 | 00111001 | 100 | 01100100 |
| 15 | 00001111 | 58 | 00111010 | 101 | 01100101 |
| 16 | 00010000 | 59 | 00111011 | 102 | 01100110 |
| 17 | 00010001 | 60 | 00111100 | 103 | 01100111 |
| 18 | 00010010 | 61 | 00111101 | 104 | 01101000 |
| 19 | 00010011 | 62 | 00111110 | 105 | 01101001 |
| 20 | 00010100 | 63 | 00111111 | 106 | 01101010 |
| 21 | 00010101 | 64 | 01000000 | 107 | 01101011 |
| 22 | 00010110 | 65 | 01000001 | 108 | 01101100 |
| 23 | 00010111 | 66 | 01000010 | 109 | 01101101 |
| 24 | 00011000 | 67 | 01000011 | 110 | 01101110 |
| 25 | 00011001 | 68 | 01000100 | 111 | 01101111 |
| 26 | 00011010 | 69 | 01000101 | 112 | 01110000 |
| 27 | 00011011 | 70 | 01000110 | 113 | 01110001 |
| 28 | 00011100 | 71 | 01000111 | 114 | 01110010 |
| 29 | 00011101 | 72 | 01001000 | 115 | 01110011 |
| 30 | 00011110 | 73 | 01001001 | 116 | 01110100 |
| 31 | 00011111 | 74 | 01001010 | 117 | 01110101 |
| 32 | 00100000 | 75 | 01001011 | 118 | 01110110 |
| 33 | 00100001 | 76 | 01001100 | 119 | 01110111 |
| 34 | 00100010 | 77 | 01001101 | 120 | 01111000 |
| 35 | 00100011 | 78 | 01001110 | 121 | 01111001 |
| 36 | 00100100 | 79 | 01001111 | 122 | 01111010 |
| 37 | 00100101 | 80 | 01010000 | 123 | 01111011 |
| 38 | 00100110 | 81 | 01010001 | 124 | 01111100 |
| 39 | 00100111 | 82 | 01010010 | 125 | 01111101 |
| 40 | 00101000 | 83 | 01010011 | 126 | 01111110 |
| 41 | 00101001 | 84 | 01010100 | 127 | 01111111 |
| 42 | 00101010 | 85 | 01010101 | 128 | 10000000 |
| 254 | 11111110 | 255 | 11111111 |
Mathematical Formulas for Converting Numbers to 8-bit Binary Code
The conversion from a decimal number to an 8-bit binary code involves expressing the decimal number as a sum of powers of 2, constrained to 8 bits (1 byte). The general formula is:
Decimal Number (D) = Σ (bi × 2i) for i = 0 to 7
Where:
- D = Decimal number (0 ≤ D ≤ 255)
- bi = Binary digit (bit) at position i, either 0 or 1
- i = Bit position index, starting from 0 (least significant bit) to 7 (most significant bit)
Each bit bi represents whether the power of two at position i is included (1) or not (0) in the sum that forms the decimal number.
To convert a decimal number to 8-bit binary:
- Start with the highest power of 2 less than or equal to the decimal number (27 = 128).
- Check if the decimal number is greater than or equal to this power.
- If yes, set the bit to 1 and subtract the power from the decimal number.
- If no, set the bit to 0.
- Repeat for the next lower power of 2 until all 8 bits are determined.
Example formula for bit extraction:
bi = floor((D / 2i) mod 2)
Where:
- floor() is the mathematical floor function (rounds down to nearest integer)
- mod is the modulo operation
This formula extracts the bit at position i by dividing the decimal number by 2i and taking the remainder modulo 2.
Detailed Explanation of Variables and Their Common Values
- D (Decimal Number): The input number to convert, ranging from 0 to 255 for 8-bit representation.
- bi (Bit at position i): Each bit can be either 0 or 1. For 8-bit binary, there are 8 bits indexed from 0 (LSB) to 7 (MSB).
- i (Bit Index): Integer from 0 to 7, representing the position of the bit in the binary number.
- 2i (Power of Two): The value of the bit position in decimal. For example, i=0 corresponds to 1, i=7 corresponds to 128.
Common values for powers of two in 8-bit binary are:
| Bit Position (i) | Power of Two (2i) |
|---|---|
| 0 | 1 |
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| 4 | 16 |
| 5 | 32 |
| 6 | 64 |
| 7 | 128 |
Real-World Examples of Converting Numbers to 8-bit Binary Code
Example 1: Encoding Sensor Data for Microcontroller Communication
Consider a temperature sensor that outputs integer values between 0 and 100 degrees Celsius. To transmit this data efficiently over a serial communication line to a microcontroller, the decimal temperature value must be converted into an 8-bit binary code.
Suppose the sensor reads 75°C. The conversion process is as follows:
- Start with the decimal number D = 75.
- Determine each bit bi using the formula: bi = floor((75 / 2i) mod 2).
| Bit Position (i) | Calculation | Bit Value (bi) |
|---|---|---|
| 7 | floor(75 / 128) mod 2 = floor(0.5859) mod 2 = 0 | 0 |
| 6 | floor(75 / 64) mod 2 = floor(1.1719) mod 2 = 1 | 1 |
| 5 | floor(75 / 32) mod 2 = floor(2.3437) mod 2 = 0 | 0 |
| 4 | floor(75 / 16) mod 2 = floor(4.6875) mod 2 = 0 | 0 |
| 3 | floor(75 / 8) mod 2 = floor(9.375) mod 2 = 1 | 1 |
| 2 | floor(75 / 4) mod 2 = floor(18.75) mod 2 = 0 | 0 |
| 1 | floor(75 / 2) mod 2 = floor(37.5) mod 2 = 1 | 1 |
| 0 | floor(75 / 1) mod 2 = floor(75) mod 2 = 1 | 1 |
Thus, the 8-bit binary code is: 01001011.
This binary code can be transmitted efficiently and decoded by the microcontroller to retrieve the original temperature value.
Example 2: Representing ASCII Characters in 8-bit Binary
ASCII characters are commonly represented using 7 or 8 bits. For example, the uppercase letter ‘A’ has a decimal ASCII code of 65. To convert this to 8-bit binary:
- D = 65
- Calculate each bit bi:
| Bit Position (i) | Calculation | Bit Value (bi) |
|---|---|---|
| 7 | floor(65 / 128) mod 2 = 0 | 0 |
| 6 | floor(65 / 64) mod 2 = 1 | 1 |
| 5 | floor(65 / 32) mod 2 = 0 | 0 |
| 4 | floor(65 / 16) mod 2 = 0 | 0 |
| 3 | floor(65 / 8) mod 2 = 0 | 0 |
| 2 | floor(65 / 4) mod 2 = 0 | 0 |
| 1 | floor(65 / 2) mod 2 = 0 | 0 |
| 0 | floor(65 / 1) mod 2 = 1 | 1 |
The resulting 8-bit binary code is 01000001, which is the standard binary representation of the ASCII character ‘A’.
Additional Technical Insights and Considerations
When working with 8-bit binary codes, it is essential to understand the limitations and implications of fixed-length binary representations:
- Range: 8-bit binary can represent unsigned integers from 0 to 255. For signed integers, the range is typically -128 to 127 using two’s complement representation.
- Padding: Numbers with fewer than 8 bits must be padded with leading zeros to maintain the 8-bit format.
- Overflow: Values exceeding 255 cannot be represented in 8 bits and require more bits or alternative encoding.
- Endianness: While endianness affects byte order in multi-byte data, it does not affect the bit order within a single 8-bit byte.
Understanding these factors is critical when designing systems that rely on binary data encoding and decoding.
Practical Applications and Industry Standards
Converting numbers to 8-bit binary code is ubiquitous in various fields:
- Embedded Systems: Microcontrollers use 8-bit registers to store and manipulate data.
- Networking: IP addresses and subnet masks often involve binary calculations at the byte level.
- Data Compression: Binary encoding schemes rely on fixed-length binary representations.
- Digital Signal Processing: Binary codes represent quantized signal values.
For authoritative references on binary encoding and digital systems, consult resources such as: