Sensible information to binary operations utilizing the UInt8 kind in Swift


Integer sorts in Swift

The Swift programming language has a bunch of various integer sorts. The Swift integer APIs have been cleaned up by an previous proposal named Protocol-oriented Integers, which resulted in a extra generic means of expressing these type of knowledge sorts.

Numeric knowledge sorts in Swift are kind secure by default, this makes a bit more durable to carry out operation utilizing totally different integer (or floating level) sorts. Integers are divided into two primary teams: signed and unsigned integers. As well as every members of those teams will be categorized by bit sizes. There are 8, 16, 32 & 64 bit lengthy signed & unsigned integers plus generic integers. 🤔

Generic integers:

  • Int (32 or 64 bit)
  • UInt (32 or 64 bit)

Signed integers:

Unsigned integers:

It’s best to know that the Int and UInt kind measurement could range on totally different platforms (32 vs 64 bits), however as a way to be constant, Apple recommends to all the time favor the generic Int kind over all the opposite variants. The Swift language all the time identifies all of the integers utilizing the Int kind by default, so in the event you maintain utilizing this kind you’ll carry out integer operations with out kind conversions, your code might be simpler to learn and it may be simpler to maneuver between platforms too. 💪

More often than not you should not care in regards to the size of the integer sorts, we will say that the generic Int and UInt sorts are very often the most effective selections whenever you write Swift code. Besides in these circumstances when your objective is to write down extraordinarily reminiscence environment friendly or low degree code…

Representing numbers as integers

Now that we all know what sort of integers can be found in Swift, it is time to speak a bit about what sort of numbers can we symbolize utilizing these knowledge sorts.


print(Int.min)      
print(Int.max)      
print(UInt.min)     
print(UInt.max)     
print(UInt8.min)    
print(UInt8.max)    
print(UInt16.min)   
print(UInt16.max)   
print(UInt32.min)   
print(UInt32.max)   
print(UInt64.min)   
print(UInt64.max)   
print(Int8.min)     
print(Int8.max)     
print(Int16.min)    
print(Int16.max)    
print(Int32.min)    
print(Int32.max)    
print(Int64.min)    
print(Int64.max)    

So there’s a minimal and most worth for every integer kind that we will retailer in a given variable. For instance, we will not retailer the worth 69420 inside a UInt8 kind, as a result of there are merely not sufficient bits to symbolize this large quantity. 🤓

Let’s look at our 8 bit lengthy unsigned integer kind. 8 bit implies that now we have actually 8 locations to retailer boolean values (ones and zeros) utilizing the binary quantity illustration. 0101 0110 in binary is 86 utilizing the “common” decimal quantity format. This binary quantity is a base-2 numerical system (a positional notation) with a radix of two. The quantity 86 will be interpreted as:

0*28+1*27+0*26+1*25+0*24 + 1*23+1*22+0*21+0*20
0*128+1*64+0*32+1*16 + 0*8+1*4+1*2+0*1
64+16+4+2
86

We will convert backwards and forwards between decimal and binary numbers, it is not that onerous in any respect, however let’s come again to this subject in a while. In Swift we will verify if a sort is a signed kind and we will additionally get the size of the integer kind by way of the bitWidth property.

print(Int.isSigned)     
print(UInt.isSigned)    
print(Int.bitWidth)     
print(UInt8.bitWidth)   

Primarily based on this logic, now it is fairly easy that an 8 bit lengthy unsigned kind can solely retailer 255 as the utmost worth (1111 1111), since that is 128+64+32+16+8+4+2+1.

What about signed sorts? Effectively, the trick is that 1 bit from the 8 is reserved for the optimistic / unfavourable image. Often the primary bit represents the signal and the remaining 7 bits can retailer the precise numeric values. For instance the Int8 kind can retailer numbers from -128 til 127, for the reason that most optimistic worth is represented as 0111 1111, 64+32+16+8+4+2+1, the place the main zero signifies that we’re speaking a few optimistic quantity and the remaining 7 bits are all ones.

So how the hack can we symbolize -128? Is not -127 (1111 1111) the minimal unfavourable worth? 😅

Nope, that is not how unfavourable binary numbers work. So as to perceive unfavourable integer illustration utilizing binary numbers, first now we have to introduce a brand new time period referred to as two’s complement, which is an easy methodology of signed quantity illustration.

Primary signed quantity maths

It’s comparatively simple so as to add two binary numbers, you simply add the bits so as with a carry, identical to you’d do addition utilizing decimal numbers. Subtraction then again is a bit more durable, however luckily it may be changed with an addition operation if we retailer unfavourable numbers in a particular means and that is the place two’s complement is available in.

We could say that we might like so as to add two numbers:

  • 0010 1010 (+42)
  • 0100 0101 +(+69)
  • 0110 1111 =(+111)

Now let’s add a optimistic and a unfavourable quantity saved utilizing two’s complement, first we have to categorical -6 utilizing a signed 8 bit binary quantity format:

  • 0000 0110 (+6)
  • 1111 1001 (one’s complement = inverted bits)
  • 1111 1010 (two’s complement = add +1 (0000 0001) to at least one’s complement)

Now we will merely carry out an addition operation on the optimistic and unfavourable numbers.

  • 0010 1010 (+42)
  • 1111 1010 +(-6)
  • (1) 0010 0100 =(+36)

So, you may assume, what is the cope with the additional 1 at first of the 8 bit end result? Effectively, that is referred to as a carry bit, and in our case it will not have an effect on our closing end result, since we have carried out a subtraction as a substitute of an addition. As you possibly can see the remaining 8 bit represents the optimistic quantity 36 and 42-6 is precisely 36, we will merely ignore the additional flag for now. 😅

Binary operators in Swift

Sufficient from the speculation, let’s dive in with some actual world examples utilizing the UInt8 kind. Initially, we should always speak about bitwise operators in Swift. In my earlier article we have talked about Bool operators (AND, OR, NOT) and the Boolean algebra, now we will say that these capabilities function utilizing a single bit. This time we will see how bitwise operators can carry out numerous transformations utilizing a number of bits. In our pattern circumstances it is all the time going to be 8 bit. 🤓

Bitwise NOT operator

This operator (~) inverts all bits in a quantity. We will use it to create one’s complement values.


let x: UInt8 = 0b00000110    
let res = ~x                 
print(res)                   
print(String(res, radix: 2)) 

Effectively, the issue is that we’ll maintain seeing decimal numbers on a regular basis when utilizing int sorts in Swift. We will print out the proper 1111 1001 end result, utilizing a String worth with the bottom of two, however for some purpose the inverted quantity represents 249 in line with our debug console. 🙃

It is because the which means of the UInt8 kind has no understanding in regards to the signal bit, and the eighth bit is all the time refers back to the 28 worth. Nonetheless, in some circumstances e.g. whenever you do low degree programming, similar to constructing a NES emulator written in Swift, that is the best knowledge kind to decide on.

The Information kind from the Basis framework is taken into account to be a set of UInt8 numbers. Really you may discover numerous use-cases for the UInt8 kind in the event you take a deeper have a look at the prevailing frameworks & libraries. Cryptography, knowledge transfers, and so forth.

Anyway, you may make an extension to simply print out the binary illustration for any unsigned 8 bit quantity with main zeros if wanted. 0️⃣0️⃣0️⃣0️⃣ 0️⃣1️⃣1️⃣0️⃣


import Basis

fileprivate extension String {
    
    func leftPad(with character: Character, size: UInt) -> String {
        let maxLength = Int(size) - rely
        guard maxLength > 0 else {
            return self
        }
        return String(repeating: String(character), rely: maxLength) + self
    }
}

extension UInt8 {
    var bin: String {
        String(self, radix: 2).leftPad(with: "0", size: 8)
    }
}

let x: UInt8 = 0b00000110   
print(String(x, radix: 2))  
print(x.bin)                
print((~x).bin)             
let res = (~x) + 1          
print(res.bin)

We nonetheless have to offer our customized logic if we wish to categorical signed numbers utilizing UInt8, however that is solely going to occur after we all know extra in regards to the different bitwise operators.

Bitwise AND, OR, XOR operators

These operators works identical to you’d anticipate it from the reality tables. The AND operator returns a one if each the bits have been true, the OR operator returns a 1 if both of the bits have been true and the XOR operator solely returns a real worth if solely one of many bits have been true.

  • AND & – 1 if each bits have been 1
  • OR | – 1 if both of the bits have been 1
  • XOR ^ – 1 if solely one of many bits have been 1
  • Let me present you a fast instance for every operator in Swift.
let x: UInt8 = 42   
let y: UInt8 = 28   
print((x & y).bin)  
print((x | y).bin)  
print((x ^ y).bin)  

Mathematically talking, there’s not a lot purpose to carry out these operations, it will not offer you a sum of the numbers or different fundamental calculation outcomes, however they’ve a distinct goal.

You should utilize the bitwise AND operator to extract bits from a given quantity. For instance if you wish to retailer 8 (or much less) particular person true or false values utilizing a single UInt8 kind you should utilize a bitmask to extract & set given components of the quantity. 😷

var statusFlags: UInt8 = 0b00000100


print(statusFlags & 0b00000100 == 4)   
print(statusFlags & 0b00010000 == 16)  
statusFlags = statusFlags & 0b11101111 | 16
print(statusFlags.bin)  
statusFlags = statusFlags & 0b11111011 | 0
print(statusFlags.bin) 
statusFlags = statusFlags & 0b11101111 | 0
print(statusFlags.bin) 
statusFlags = statusFlags & 0b11101011 | 4
print(statusFlags.bin) 

That is good, particularly in the event you do not wish to fiddle with 8 totally different Bool variables, however one there’s one factor that may be very inconvenient about this answer. We all the time have to make use of the best energy of two, after all we may use pow, however there’s a extra elegant answer for this difficulty.

Bitwise left & proper shift operators

By utilizing a bitwise shift operation you possibly can transfer a bit in a given quantity to left or proper. Left shift is actually a multiplication operation and proper shift is equivalent with a division by an element of two.

“Shifting an integer’s bits to the left by one place doubles its worth, whereas shifting it to the best by one place halves its worth.” – swift.org

It is fairly easy, however let me present you just a few sensible examples so you may perceive it in a bit. 😅

let meaningOfLife: UInt8 = 42



print(meaningOfLife << 1) 
print(meaningOfLife << 2) 
print(meaningOfLife << 3) 
print(meaningOfLife >> 1) 
print(meaningOfLife >> 2) 
print(meaningOfLife >> 3) 
print(meaningOfLife >> 4) 
print(meaningOfLife >> 5) 
print(meaningOfLife >> 6) 
print(meaningOfLife >> 7) 

As you possibly can see now we have to watch out with left shift operations, for the reason that end result can overflow the 8 bit vary. If this occurs, the additional bit will simply go away and the remaining bits are going for use as a closing end result. Proper shifting is all the time going to finish up as a zero worth. ⚠️

Now again to our standing flag instance, we will use bit shifts, to make it extra easy.

var statusFlags: UInt8 = 0b00000100


print(statusFlags & 1 << 2 == 1 << 2)


statusFlags = statusFlags & ~(1 << 2) | 0
print(statusFlags.bin)


statusFlags = statusFlags & ~(1 << 2) | 1 << 2
print(statusFlags.bin)

As you possibly can see we have used numerous bitwise operations right here. For the primary verify we use left shift to create our masks, bitwise and to extract the worth utilizing the masks and eventually left shift once more to match it with the underlying worth. Contained in the second set operation we use left shift to create a masks then we use the not operator to invert the bits, since we will set the worth utilizing a bitwise or operate. I suppose you possibly can work out the final line primarily based on this data, but when not simply follow these operators, they’re very good to make use of as soon as all of the little the small print. ☺️

I feel I’ll minimize it right here, and I will make simply one other publish about overflows, carry bits and numerous transformations, perhaps we’ll contain hex numbers as effectively, anyway do not wish to promise something particular. Bitwise operations are usueful and enjoyable, simply follow & do not be afraid of a little bit of math. 👾

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