Arnab Das Arnab Das - 1 year ago 67
Scala Question

Scala Byte type can contain -128 but not 128

I'm new to Scala. I've encountered a strange fact that it's

type can contain -128 but not 128.

scala> val overflow1NegByte = -129:Byte
<console>:11: error: type mismatch;
found : Int(-129)
required: Byte
val overflow1NegByte = -129:Byte

scala> val overflow1NegByte = -128:Byte
overflow1NegByte: Byte = -128

scala> val overflow1PosByte = 128:Byte
<console>:11: error: type mismatch;
found : Int(128)
required: Byte
val overflow1PosByte = 128:Byte

scala> val overflow1PosByte = 127:Byte
overflow1PosByte: Byte = 127

Apparently it feels that, to indicate a negative number, first flag is used. For positive numbers also this flag is reserved. This is understandable. But, why one more negative number than the positives.

Answer Source

Because that's the range of a Byte on the JVM:

byte: The byte data type is an 8-bit signed two's complement integer. It has a minimum value of -128 and a maximum value of 127 (inclusive).

As explained, this is because of Two's Complement.

Let's explain a bit more. A byte holds 8 bits, and if we wanted to represent the number -128. We start from 128:


And we invert the bits:


And add 1. We get back:


This is how -128 is represented. This means that the biggest signed number we can represent with Twos Complement is:


Which is equivalent to 127.

From wikipedia:

An N-bit two's-complement numeral system can represent every integer in the range −(2N − 1) to +(2N − 1 − 1)

So, we have:

-(2^7-1) = (-128) to +(2^7-1 - 1) = +(127) 
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