Roman Numeral Conversion

Roman Numeral Conversion Functions

by Stephen R. Schmitt

Conversion Principles

Roman numerals are converted mathematically by simply assigning a numerical value to each letter and calculating a total where:

M = 1000
D =  500
C =  100
L =   50
X =   10
V =    5
I =    1

Letters are arranged from left to right in order of decreasing value. The total is the numerical values of all the letters in the sequence. For example,

XVI = 10 + 5 + 1 = 16

However, the subtraction principle requires that a lower numeral appearing before a higher one be subtracted from the higher value, not added to the total. For example,

XIX = X + IX = 10 + 9 = 19

rather than 21, which is written as

XXI = 10 + 10 + 1 = 21

Similarly, the Roman numeral for the year 1948 is usually written as

MCMXLVIII = M + CM + XL + VIII = 1000 + 900 + 40 + 8 = 1948

Zeno source code

Zeno 1.2 is an interpreter for the Zeno programming language. It is an easy to learn and is suitable for educational purposes.

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function roman2int( str : string ) : int

    var i, j, k : int
    var val : int := 0
    var len : int := strlen( str )

    if len = 0 then
        return -1
    end if

    k := -1
    for i := 1...len do

        % get char value
        case str[i] of
        value 'I', 'i':  j := 1
        value 'V', 'v':  j := 5
        value 'X', 'x':  j := 10
        value 'L', 'l':  j := 50
        value 'C', 'c':  j := 100
        value 'D', 'd':  j := 500
        value 'M', 'm':  j := 1000
        value:           return -1
        end case

        % add increment
        if (k >= 1) and (k < j) then
            val := val - k*2
            val := val + j
        else
            val := val + j
        end if

        % save prev char value
        k := j

    end for

    return val

end function

function int2roman( in : int ) : string

    var wh : string := "IVXLCDM"    
    var number, divisor : int
    var i, j, k, p : int
    var str : string

    number := in
    divisor := 1000
    p := 1

    for decreasing k := 3 ... 0 do
        i := number div divisor
        number := number mod divisor
        case i of
        value 0:
            % do nothing
        value 5:
            str[p] := wh[2*k+2]
            p := p + 1
        value 9:
            str[p] := wh[2*k+1]
            p := p + 1
            str[p] := wh[2*k+3]
            p := p + 1
        value 4:
            str[p] := wh[2*k+1]
            p := p + 1
            str[p] := wh[2*k+2]
            p := p + 1
        value : 
            if i > 5 then
                str[p] := wh[2*k+2]
                p := p + 1
                i := i - 5
            end if
            for j := 0 ... i-1 do
                str[p] := wh[2*k+1]
                p := p + 1
            end for
        end case
        divisor := divisor div 10
    end for
    str[p] := chr( 0 )

    return str

end function

Sample output

integer? 1948
MCMXLVIII

Roman numeral? MCMXLVIII
1948

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