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Cannot convert from to - Java's implicit type conversion and an unary operator

byte b1 = 3 + 5;
The literals 3, 5 and 3 + 5 are of type int.
The expression above works because Java internally converts the result of 3 + 5 from int to byte, or?
The same explanation should work in the case of b2:
byte b1 = 3 + 5;
byte b2 = b1 + 5; // Type mismatch: cannot convert from int to byte
But it does not.
Why?

The operands of + undergo binary numeric promotion: that is, they are widened where necessary to make them compatible for addition. The rule is quite simple:
If either operand is a double, widen the other to double
If either operand is a float, widen the other to float
If either operand is a long, widen the other to long
Otherwise, widen them both to int
in the second case, it is effectively (int) b1 + 5, the result of which is a non-compile-time constant int. This can't be guaranteed to be in the range of byte, so the compiler complains.
In the first case, both operands are compile-time constant ints, so the result is a compile-time constant int; the compiler can check that result is within the range of byte, and so can implicitly narrow the result.

ints are implicitly cast to bytes in your previous assignments, to mimic the effect in the last statement you need to do it explicitly after java promotes b1 + 5 to an int, like this:
byte b2 = (byte) b1 + 5;
alternatively if you declare b1 as final, the compiler will check the ranges and do the assignment (with an implicit cast) as you expected originally, since 3 + 5it is in the range of bytes and b1 will not be changing its value (3):
final byte b1 = 3;
byte b2 = b1 + 5;

Different result with same if / else condition [duplicate]

I have seen it discussed somewhere that the following code results in obj being a Double, but that it prints 200.0 from the left hand side.
Object obj = true ? new Integer(200) : new Double(0.0);
System.out.println(obj);
Result: 200.0
However, if you put a different object in the right hand side, e.g. BigDecimal, the type of obj is Integer as it should be.
Object obj = true ? new Integer(200) : new BigDecimal(0.0);
System.out.println(obj);
Result: 200
I presume that the reason for this is something to do with casting the left hand side to a double in the same way that it happens for integer/double comparisons and calculations, but here the left and right sides do not interact in this way.
Why does this happen?

You need to read section 15.25 of the Java Language Specification.
In particular:
Otherwise, if the second and third operands have types that are convertible (§5.1.8) to numeric types, then there are several cases:
If one of the operands is of type byte or Byte and the other is of type short or Short, then the type of the conditional expression is short.
If one of the operands is of type T where T is byte, short, or char, and the other operand is a constant expression of type int whose value is representable in type T, then > - the type of the conditional expression is T.
If one of the operands is of type Byte and the other operand is a constant expression of type int whose value is representable in type byte, then the type of the conditional expression is byte.
If one of the operands is of type Short and the other operand is a constant expression of type int whose value is representable in type short, then the type of the conditional expression is short.
If one of the operands is of type; Character and the other operand is a constant expression of type int whose value is representable in type char, then the type of the conditional expression is char.
Otherwise, binary numeric promotion (§5.6.2) is applied to the operand types, and the type of the conditional expression is the promoted type of the second and third operands. Note that binary numeric promotion performs unboxing conversion (§5.1.8) and value set conversion (§5.1.13).
So binary numeric promotion is applied, which starts with:
When an operator applies binary numeric promotion to a pair of operands, each of which must denote a value that is convertible to a numeric type, the following rules apply, in order, using widening conversion (§5.1.2) to convert operands as necessary:
If any of the operands is of a reference type, unboxing conversion (§5.1.8) is performed. Then:
If either operand is of type double, the other is converted to double.
That's exactly what happens here - the parameter types are converted to int and double respectively, the second operand (the third in the original expression) is then of type double, so the overall result type is double.

Numeric conversion in the conditional operator ? :
In the conditional operator a?b:c, if both b and c are different numeric types, the following conversion rules are applied at compile time to make their types equal, in order:
The types are converted to their corresponding primitive ones, which is called unboxing.
If one operand were a constant int (not Integer before unboxing) whose value is representable in the other type, the int operand is converted into the other type.
Otherwise the smaller type is converted into the next greater one until both operands have the same type. The conversion orders are:
byte -> short -> int -> long -> float -> double
char -> int -> long -> float -> double
Eventually the whole conditional expression gets the type of its second and third operands.
Examples:
If you combine char with short, the expression becomes int.
If you combine Integer with Integer, the expression becomes Integer.
If you combine final int i = 5 with a Character, the expression becomes char.
If you combine short with float, the expression becomes float.
In the question's example, 200 is converted from Integer into double, 0.0 is unboxed from Double into double and the whole conditional expression becomes becomes double which is eventually boxed into Double because obj is of type Object.

Example:
public static void main(String[] args) {
int i = 10;
int i2 = 10;
long l = 100;
byte b = 10;
char c = 'A';
Long result;
// combine int with int result is int compiler error
// result = true ? i : i2; // combine int with int, the expression becomes int
//result = true ? b : c; // combine byte with char, the expression becomes int
//combine int with long result will be long
result = true ? l : i; // success - > combine long with int, the expression becomes long
result = true ? i : l; // success - > combine int with long, the expression becomes long
result = true ? b : l; // success - > combine byte with long, the expression becomes long
result = true ? c : l; // success - > char long with long, the expression becomes long
Integer intResult;
intResult = true ? b : c; // combine char with byte, the expression becomes int.
// intResult = true ? l : c; // fail combine long with char, the expression becomes long.
}

Multiplying two bytes

Can somebody explain me why I can't to multiply two bytes in this way?
byte a = 1;
byte b = 1;
byte c = a*b;
or
byte a = 1;
byte b = 1;
short c = a*b;
Why I have to do that in this way?
byte a = 1;
byte b = 1;
byte c = (byte)(a*b);
or
byte a = 1;
byte b = 1;
int/double/float/long c = a*b;

When performing math with bytes, binary numeric promotion takes place, as specified by the JLS, Section 5.6.2.
When an operator applies binary numeric promotion to a pair of operands, each of which must denote a value that is convertible to a numeric type, the following rules apply, in order:
If any operand is of a reference type, it is subjected to unboxing conversion (§5.1.8).
Widening primitive conversion (§5.1.2) is applied to convert either or both operands as specified by the following rules:
If either operand is of type double, the other is converted to double.
Otherwise, if either operand is of type float, the other is converted to float.
Otherwise, if either operand is of type long, the other is converted to long.
Otherwise, both operands are converted to type int.
(emphasis mine)
That forces you to assign to a type that is at least as wide as int or to cast back to byte.

Product of two bytes will not necessarily fit into a byte. So Java needs you to tell it that you know what you are doing and confirm that in case of overflow you will get the low-order bits.

Rules for typecasting with byte

I was just playing around with type casting. Here's the code:
class Typecasting {
public static void main(String[] args) {
byte b = 3;
byte c = b++; // no error
byte d = b + 1; // error
byte e = b + b; // error
}
}
Why is there no error in the first line but in second?? Also when i do
f = b + 2;
I understand that b was automatically cast into int type and therefore f must be int type but when I do
e = b + b;
they both are byte type and their result is also in the range of a byte, so why can't e have byte data type? Is it due to the + binary operator?

Why is there no error in the first line but in second?
Because that's the way the language is defined. There's no byte + byte operator, which is why the third line fails - both operands are promoted to int automatically. From section 15.18.2 of the JLS:
The binary + operator performs addition when applied to two operands of numeric type, producing the sum of the operands.
...
Binary numeric promotion is performed on the operands (§5.6.2).
Now binary numeric promotion always ends up with a value of int, long, float or double... int in this case. So the operation is to add two int values together, and the result is an int.
For b++, however, the type is still byte. It's a postfix increment expression (section 15.14.2):
The type of the postfix increment expression is the type of the variable.
On a related note, this would be okay:
b += 3;
That's a compound assignment (section 15.26.2):
A compound assignment expression of the form E1 op= E2 is equivalent to E1 = (T) ((E1) op (E2)), where T is the type of E1, except that E1 is evaluated only once.
Note the casting part, which is why it works.

+(byte, byte) returns an int per the rules of the language.
The relevant section of the spec is §5.6.2:
When an operator applies binary numeric promotion to a pair of operands, each of which must denote a value that is convertible to a numeric type, the following rules apply, in order, using widening conversion (§5.1.2) to convert operands as necessary:
If any of the operands is of a reference type, unboxing conversion (§5.1.8) is performed. Then:
If either operand is of type double,the other is converted to double.
Otherwise, if either operand is of type float, the other is converted to float.
Otherwise, if either operand is of type long, the other is converted to long.
Otherwise, both operands are converted to type int.
Whereas for ++, the type of the result is the type of the operand. From the JLS, §15.14.2:
The type of the postfix increment expression is the type of the variable.
Thus, for b++, the result is a byte and so is assignable to c.

byte d = b+1;
In here you are assign int value(b+1) to byte d. When you added a int vale to byte value it becomes int value.

byte c = b++; //No error;First Line
This conforms to JLS 15.14.2
The type of the postfix increment expression is the type of the variable. The result of the postfix increment expression is not a variable, but a value.
byte d = b+1; //error;Second Line
byte e = b+b; //error;Third line
This conforms to JLS 15.18.2
The binary + operator performs addition when applied to two operands of numeric type, producing the sum of the operands.
The type of an additive expression on numeric operands is the promoted type of its operands.
If this promoted type is int or long, then integer arithmetic is performed.
Read about type promotion in JLS 5.6.2
Widening primitive conversion (§5.1.2) is applied to convert either or both operands as specified by the following rules:
If either operand is of type double, the other is converted to double.
Otherwise, if either operand is of type float, the other is converted to float.
Otherwise, if either operand is of type long, the other is converted to long.
Otherwise, both operands are converted to type int.

in line first ++operator returns always operand type result..so it gives no error
in second line here 1 is an integer type because all integer type literals is int by default
in third line +(byte,byte) returns the integer type that why it will forces you to type cast it into int.
--> in third line there is always a probability to overflow in byte type..
* if your byte type is defined as constant then it will not force you to typecast because it will alwayz be in range.

When Java performs a sum, it first "transforms" both operands to int or long (depending of the operands) and the result will be an integer, which will try to assign to your variable of type byte, as it "realizes" the result wont fit in a byte, then it will "complain" and you wont be even able to compile this.

Casting characters in Java

I am learning Java. I found that expressions often have to be cast to a certain type in order to do it right. For example, during arithmetic evaluation, bytes are promoted to integers, so the following expression will throw an error:
byte b = 10;
int i;
i = b*b; //ok, assigning an integer evaluation to an integer variable
b = b*b; // throws error, coz assigning integer evaluation to byte variable
Now, I know that assigning an integer to a character variable is all right: char a; a = 88; is okay. However, if I do this:
char c2 = 'b', c3 = 'c';
c2 = c2 + c3; //throws error
c2 = (char)(c2 + c3); //works fine
Why does it throw an error when not casted? After all, the right hand side is still an integer, so assigning an integer to a character variable should work just fine.

In c2 + c3, both operands are implicitly widened to int, so the result of the addition is also an int.
JLS §15.18.2. Additive Operators (+ and -) for Numeric Types:
Binary numeric promotion is performed on the operands (§5.6.2).
JLS §5.6.2. Binary Numeric Promotion:
When an operator applies binary numeric promotion to a pair of operands, each of which must denote a value that is convertible to a numeric type, the following rules apply, in order:
Widening primitive conversion (§5.1.2) is applied to convert either or both operands as specified by the following rules:
If either operand is of type double, the other is converted to double.
Otherwise, if either operand is of type float, the other is converted to float.
Otherwise, if either operand is of type long, the other is converted to long.
Otherwise, both operands are converted to type int.
You therefore end up with an int. Assigning it to a char variable requires an explicit cast.
You say:
Since integer value can be assigned to a character variable...
Only constant integer expressions can be assigned to a char variable without a cast.
JLS §5.2. Assignment Conversion:
In addition, if the expression is a constant expression (§15.28) of type byte, short, char, or int:
A narrowing primitive conversion may be used if the type of the variable is byte, short, or char, and the value of the constant expression is representable in the type of the variable.
This automatic narrowing conversion doesn't apply here. You need an explicit cast.

It does not necessarily work fine to assign an int to a char. Chars are only 16 bit and ints are 32 bit, so the there might be an overflow.
In general Java only allows assignment of primitives values without cast if no overflow can occur as a result of the assignment.

char c2 = 'b', c3 = 'c';
c2 = c2 + c3; //throws error
c2 = (char)(c2 + c3); //works fine
when you doing c2+ c3
ASCII value of these chars are added which returns a int result.
when you are assigning int result to char it gives error.

Assigning an int 88 to a char works, because the compiler can determine the value.
The case c2 = c2 + c3 cannot be handled by the compiler. The value c2 + c3 must be evaluated at run time. Therefore, the compiler cannot determine the actual char value that has to be assigned.

char is 2 bytes and int is 4 bytes. When you write char c = 1; it does not mean that 1 is int, it's just a constant for javac and javac knows that 1 fits into char. But c2 = c2 + c3; is arithmetic operation, javac will interprets it as (int)c2 + (int)c3 and this produces int result. int does not fit into char so javac warns you that there may be lost of precision.

Have a look at thread:
Integer arithmetic in Java with char and integer literal
The reason seems to be that "c2 = c2 + c3;" cannot be checked by the compiler (it is executed in runtime) whereas "char a; a = 88;" is directly done by the compiler.

An example for further clarification:
char c1 = Character.MAX_VALUE;
char c2 = Character.MAX_VALUE;
char c3 = (char) (c1 + c2);
int i3 = c1 + c2;
System.out.printf("After casting to char: %s, the int value: %s%n", (int) c3, i3);
So with casting we actually got a wrong mathematical result.

There is a certain limit as to how much value each basic type can hold in java.Assigning the result of an arithmetic operation can produce an unpredictable result at run-time ,which JVM is unsure if char can hold,therefore the compilation error.