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 signify utilizing these knowledge 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 won’t retailer the worth 69420 inside a UInt8 sort, as a result of there are merely not sufficient bits to signify this big quantity. 🤓

Let’s look at our 8 bit lengthy unsigned integer sort. 8 bit signifies that we’ve got 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 could 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 forwards and backwards between decimal and binary numbers, it isn’t that tough in any respect, however let’s come again to this subject afterward. In Swift we are able to verify 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 easy 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 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 sort 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 couple of optimistic quantity and the remaining 7 bits are all ones.

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

Nope, that is not how unfavourable binary numbers work. With the intention to perceive unfavourable integer illustration utilizing binary numbers, first we’ve got to introduce a brand new time period referred to as two’s complement, which is an easy technique of signed quantity illustration.

Primary signed quantity maths

It’s comparatively straightforward 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 tougher, however happily 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 complenet = add +1 (0000 0001) to 1’s complement)

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

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

So, you would possibly assume, what is the take care of the additional 1 to start with of the 8 bit consequence? Nicely, that is referred to as a carry bit, and in our case it will not have an effect on our last consequence, since we have carried out a subtraction as an alternative of an addition. As you may see the remaining 8 bit represents the optimistic quantity 36 and 42-6 is strictly 36, we are able to 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 sort. Initially, we should always discuss 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 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)) 

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 right 1111 1001 consequence, utilizing a String worth with the bottom of two, however for some purpose the inverted quantity represents 249 in response to 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 all the time refers back to the 2⁸ worth. Nonetheless, in some circumstances e.g. while you do low stage programming, reminiscent of constructing a NES emulator written in Swift, that is the suitable knowledge sort to decide on.

The Knowledge sort 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 sort in case you take a deeper take a look at the prevailing frameworks & libraries. Cryptography, knowledge transfers, and so on.

Anyway, you can also 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 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 count on it from the reality tables. The AND operator returns a one if each the bits had been true, the OR operator returns a 1 if both of the bits had been true and the XOR operator solely returns a real worth if solely one of many bits had been true.

• AND & – 1 if each bits had been 1
• OR | – 1 if both of the bits had been 1
• XOR ^ – 1 if solely one of many bits had 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 primary calculation outcomes, however they’ve a special goal.

You should 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 need to use 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 case you do not wish to fiddle with 8 completely different Bool variables, however one there’s one factor that may be very inconvenient about this resolution. We all the time have to make use of the suitable energy of two, in fact we might use pow, however there’s a extra elegant resolution for this difficulty.

Bitwise left & proper shift operators

By utilizing a bitwise shift operation you may 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 suitable by one place halves its worth.” – swift.org

It is fairly easy, however let me present you a number 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 may see we’ve got 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 last consequence. Proper shifting is all the time 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 may 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 perform. I suppose you may determine the final line based mostly on this information, but when not simply apply these operators, they’re very good to make use of as soon as all of the little the small print. ☺️

I believe I will reduce it right here, and I am going to make simply one other put up about overflows, carry bits and numerous transformations, possibly we’ll contain hex numbers as effectively, anyway do not wish to promise something particular. Bitwise operations are usueful and enjoyable, simply apply & do not be afraid of a little bit of math. 👾