Sensible information to binary operations utilizing the UInt8 sort in Swift

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 information varieties.

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 sort that we are able to retailer in a given variable. For instance, we will not retailer the worth 69420 inside a UInt8 sort, 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 sort. 8 bit implies that we now 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 may 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 isn’t that arduous in any respect, however let’s come again to this subject afterward. In Swift we are able to test if a sort is a signed sort and we are able to additionally get the size of the integer sort via the bitWidth property.

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

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

What about signed varieties? Nicely, the trick is that 1 bit from the 8 is reserved for the constructive / unfavourable image. Normally the primary bit represents the signal and the remaining 7 bits can retailer the precise numeric values. For instance the Int8 sort can retailer numbers from -128 til 127, for the reason that most constructive worth is represented as 0111 1111, 64+32+16+8+4+2+1, the place the main zero signifies that we’re speaking a couple of constructive 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. With a purpose to perceive unfavourable integer illustration utilizing binary numbers, first we now have to introduce a brand new time period known as two’s complement, which is a straightforward methodology of signed quantity illustration.

Fundamental signed quantity maths

It’s comparatively simple so as to add two binary numbers, you simply add the bits so as with a carry, similar to you’d do addition utilizing decimal numbers. Subtraction alternatively is a bit tougher, however happily it may be changed with an addition operation if we retailer unfavourable numbers in a particular approach and that is the place two’s complement is available in.

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

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

Now let’s add a constructive 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 complenet = add +1 (0000 0001) to at least one’s complement)

Now we are able to merely carry out an addition operation on the constructive and unfavourable numbers.

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

So, you may assume, what is the take care of the additional 1 to start with of the 8 bit consequence? Nicely, that is known as a carry bit, and in our case it will not have an effect on our remaining consequence, since we have carried out a subtraction as a substitute of an addition. As you possibly can see the remaining 8 bit represents the constructive quantity 36 and 42-6 is precisely 36, we are able to merely ignore the additional flag for now. 😅

Binary operators in Swift

Sufficient from the idea, let’s dive in with some actual world examples utilizing the UInt8 sort. To begin with, we must 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 are able to say that these features function utilizing a single bit. This time we will see how bitwise operators can carry out varied transformations utilizing a number of bits. In our pattern circumstances it is at all times 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)) 

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

It’s because the which means of the UInt8 sort has no understanding in regards to the signal bit, and the eighth bit is at all times refers back to the 2⁸ worth. Nonetheless, in some circumstances e.g. if you do low stage programming, corresponding to constructing a NES emulator written in Swift, that is the fitting information sort to decide on.

The Knowledge sort from the Basis framework is taken into account to be a group of UInt8 numbers. Truly you may discover various use-cases for the UInt8 sort for those who take a deeper take a look at the present frameworks & libraries. Cryptography, information transfers, and so on.

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) - depend
        guard maxLength > 0 else {
            return self
        }
        return String(repeating: String(character), depend: 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 supply 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 similar 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 cause to carry out these operations, it will not offer you a sum of the numbers or different fundamental calculation outcomes, however they’ve a unique objective.

You need to use 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 sort you should utilize a bitmask to extract & set given elements 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 for those who do not wish to fiddle with 8 completely different Bool variables, however one there’s one factor that could be very inconvenient about this resolution. We at all times have to make use of the fitting energy of two, after all we may use pow, however there’s a extra elegant resolution for this situation.

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 basically 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 fitting by one place halves its worth.” – swift.org

It is fairly easy, however let me present you a couple of 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 we now have to watch out with left shift operations, for the reason that consequence 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 remaining consequence. Proper shifting is at all times going to finish up as a zero worth. ⚠️

Now again to our standing flag instance, we are able to 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 various bitwise operations right here. For the primary test 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 observe these operators, they’re very good to make use of as soon as you realize all of the little the main points. ☺️

I feel I’ll lower it right here, and I am going to make simply one other submit about overflows, carry bits and varied transformations, possibly we’ll contain hex numbers as nicely, anyway do not wish to promise something particular. Bitwise operations are usueful and enjoyable, simply observe & do not be afraid of a little bit of math. 👾