APL (Dyalog Unicode), 4 bytes^SBCS

Anonymous tacit prefix function. Takes [a,b,c,d] as argument. Returns a bit-Boolean array.*

⌈/=⌽

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⌈/ Does the maximum of the argument

= equal (vectorises)

⌽ the reverse of the argument?

* Note that APL stores arrays of Booleans using one bit per value, so this does indeed return a 4-bit word, despite the display form being 0 0 1 0.

R, 17 bytes

max(a<-scan())==a

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Returns a vector of booleans. Since this output has been confirmed, this is preferable over numerical output, as that one is almost twice longer:

R, 33 bytes

sum(2^which(max(a<-scan())==a)/2)

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Japt, 5

£Â(X¶UrÈwY

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-4 bytes thanks to @Oliver!

-2 bytes thanks to @Shaggy!

Input is a 4-element array in the following format:

[d, c, b, a]

Output is an array of bits.

JavaScript (ES6), 40 bytes

Takes input as ([d,c,b,a]).

a=>a.map(r=x=>r=r*2|x==Math.max(...a))|r

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Or 30 bytes if we can return 4 Boolean values:

a=>a.map(x=>x==Math.max(...a))

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05AB1E, 3 bytes

ZQR

Input as a list of [a,b,c,d], output as a list of boolean.

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If this output format is not allowed based on the hexadecimal that is used in the challenge description, it would be 6 bytes instead:

ZQRJCh

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Explanation:

Z    # Take the maximum of the implicit input-list

 Q   # Check for each in the (implicit) input-list if it equals this value

  R  # Reverse the resulting list (and output implicitly as result)



J    # Join the list of 0s and 1s to a single string

 C   # Convert from binary to integer

  h  # Convert from integer to hexadecimal (and output implicitly as result)

Perl 6, 12 bytes

{$_ X==.max}

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Anonymous code block that takes a list of integers and returns a list of booleans. If we need to return as a number, it's +4 bytes to wrap the inside of the code block with 2:[...].

Explanation:

{          }  # Anonymous code block

 $_           # With the input

    X==       # Which values are equal

       .max   # To the maximum element

Haskell, 47 bytes

a#b=sum[1|b]+2*a

foldl(#)0.(map=<<(==).maximum)

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35 bytes if I can output a string

f x=show.fromEnum.(==maximum x)=<<x

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C# (Visual C# Interactive Compiler), 39 bytes

n=>n.Select((a,b)=>n[3-b]==n.Max()?1:0)

Returns an IEnumerable<int>, which represent bits.

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C# (Visual C# Interactive Compiler), 35 bytes

n=>n.Select((a,b)=>n[3-b]==n.Max())

If an IEnumerable<bool> is acceptable.

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C# (Visual C# Interactive Compiler), 49 bytes

n=>{for(int i=4;i-->0;Write(n[i]==n.Max()?1:0));}

Prints a binary string to STDOUT.

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Python 3.8 (pre-release), 67 bytes

Lambda function that takes in 4 integers, bit shifts the boolean result of their comparison to the maximum value with some help from Python 3.8's new assignment operator, and returns the bitwise OR of the results

lambda a,b,c,d:((m:=max(a,b,c,d))==d)<<3|(m==c)<<2|(m==b)<<2|(a==m)

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PHP, 54 bytes

while($i<4)$argv[++$i]<max($argv)||$r+=1<<$i-1;echo$r;

or

while($i<4)$argv[++$i]<max($argv)||$r+=1<<$i;echo$r/2;

take input from command line arguments. Run with -nr or try them online.

Here's a JS version that outputs as binary

update: Shorter with join, and without the lookup:

JavaScript (Node.js), 42 bytes

a=>a.map(x=>+(x==Math.max(...a))).join('')

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Previous, with lookup, 49 bytes

a=>a.map(x=>[0,1][+(x==Math.max(...a))]).join('')

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Previous, with reduce, 52 bytes:

a=>a.reduce((y,x)=>y+[0,1][+(x==Math.max(...a))],'')

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fa=>a.map(x=>+(x==Math.max(...a))).join('')

console.log(f([ 4, 1,77, 6])) // 0010

console.log(f([10,10, 5, 4])) // 1100

console.log(f([ 1, 1, 1, 1])) // 1111

C# (Visual C# Interactive Compiler), 51 bytes

x=>{for(int m=x.Max(),i=4;i-->0;)x[i]=x[i]==m?1:0;}

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Above is an anonymous function that outputs by modifying an argument. Output is an array of 1's and 0's.

Below is a recursive function that outputs an integer.

C# (Visual C# Interactive Compiler), 60 bytes

int f(int[]x,int i=3)=>i<0?0:2*f(x,i-1)|(x[i]==x.Max()?1:0);

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Both functions take input as a 4-element array.

[d, c, b, a]

Java (JDK), 78 bytes

a->{int m=a[0],w=1,p=1;for(int t:a){w=t<m?w:p|(t>m?(m=t)^m:w);p*=2;}return w;}

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• Takes the input as an array of [a,b,c,d].

Ruby, 34 bytes

Takes input as an array [d, c, b, a] and returns an integer.

->r{r.reduce(0){|m,o|o/r.max+m*2}}

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Python 2, 35 bytes

lambda i:[int(x==max(i))for x in i]

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Takes input in the format [d,c,b,a] as with the accepted answer from Adám so I guess it is OK.

Alternative for 41 if it's not...

Python 2, 41 bytes

lambda i:[int(x==max(i))for x in i][::-1]

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