Base Conversions
| Type | Quiz 1 Material |
|---|
Notes
Conversions
Binary to Decimal
Visual Representation:
| Decimal | Binary | Arithmetic |
| 0 | 0000 | 0+0+0+0 |
| 1 | 0001 | 0+0+0+1 |
| 2 | 0010 | 0+0+2+0 |
| 3 | 0011 | 0+0+2+1 |
| 4 | 0100 | 0+4+0+0 |
| 5 | 0101 | 0+4+0+1 |
| 6 | 0110 | 0+4+2+0 |
| 7 | 0111 | 0+4+2+1 |
| 8 | 1000 | 8+0+0+0 |
| 9 | 1001 | 8+0+0+1 |
| 10 | 1010 | 8+0+2+0 |
| 11 | 1011 | 8+0+2+1 |
| 12 | 1100 | 8+4+0+0 |
| 13 | 1101 | 8+4+0+1 |
| 14 | 1110 | 8+4+2+0 |
| 15 | 1111 | 8+4+2+1 |
0b010101110 is sometimes used for binary, but is not standard in Java and C
// Does not include negative numbers
public static int binaryStringToInt(String binary) {
int output = 0;
for (int i = 0; i < binary.length(); i++) {
if (binary.charAt(i) == '1') {
output += 1 << binary.length() - i - 1;
}
}
return output;
}Binary to Octal
Diagram:
| Base 2 | 000 | 111 | 010 | 100 | 101 |
| Base 8 | 0 | 7 | 2 | 4 | 5 |
public static String binaryStringToOctalString(String binary) {
int decimal = 0;
for (int i = 0; i < binary.length(); i++) {
if (binary.charAt(i) == '1') {
decimal += 1 << binary.length() - i - 1;
}
}
String output = "";
int counter = 21;
for (int i = 7; i >= 0; --i) {
output += (decimal >> counter) & 0b111;
counter -= 3;
}
return output;Binary to Hexadecimal
Diagram:
| Base 2 | 1000 | 1111 | 0011 | 1100 | 0001 |
| Base 8 | 8 | F | 3 | C | 1 |
Decimal to Binary
Decimal to Octal
Decimal to Hexadecimal
public static String intToHexString(int hex) {
String output = "";
int counter = 16;
while (counter <= hex) {
counter = counter << 4;
}
counter = counter >> 4;
int counter2 = 0;
while (counter != 0) {
if (hex < counter) {
if (counter2 > 9) {
output += (char)(counter2 + 65 - 10);
} else {
output += counter2;
}
counter = counter >> 4;
counter2 = 0;
}
hex -= counter;
counter2++;
}
return output;
}Octal to Binary
| Base 8 | 6 | 4 | 3 | 0 | 2 |
| Base 2 | 110 | 100 | 011 | 000 | 010 |
0456 is octal
Octal to Decimal
public static int octalStringToInt(String octal) {
int output = 0, counter = 0;
for (int i = octal.length() - 1; i > -1; i--) {
output += (octal.charAt(i) - 48) << counter;
counter += 3;
}
return output;
}Octal to Hexadecimal
Hexadecimal to Binary
Diagram Example:
| Base 16 | F | 0 | 0 | D | 5 |
| Base 2 | 1111 | 0000 | 0000 | 1101 | 0101 |
0x456 is hexadecimal
Hexadecimal to Decimal
Hexadecimal to Octal
Bonus Info
Converting base 10 string to int:
public static int decimalStringToInt(String decimal) {
int output = 0, counter = 1;
for (int i = decimal.length() - 1; i > -1; i--) {
output += (decimal.charAt(i) - 48) * counter;
counter *= 10;
}
return output;
}Powers of 2
| 2^n | literal value |
| 2^0 | 1 |
| 2^1 | 2 |
| 2^2 | 4 |
| 2^3 | 8 |
| 2^4 | 16 |
| 2^5 | 32 |
| 2^6 | 64 |
| 2^7 | 128 |
| 2^8 | 256 |
| 2^9 | 512 |
| 2^10 | 1024 |
| 2^11 | 2048 |
| 2^12 | 4096 |
| 2^13 | 8192 |
| 2^14 | 16384 |
| 2^15 | 32768 |
| 2^16 | 65536 |
Questions & Answers
How many different numbers can be represented by n bits?
2^n
What are the tricks to doing conversions in between binary/octal/hexadecimal (larger numbers) quickly?