function addStrings(a, b)
    local carry = 0
    local result = {}
    local lenA, lenB = #a, #b
    local maxLen = math.max(lenA, lenB)

    a = string.rep("0", maxLen - lenA) .. a
    b = string.rep("0", maxLen - lenB) .. b

    for i = maxLen, 1, -1 do
        local sum = tonumber(a:sub(i, i)) + tonumber(b:sub(i, i)) + carry
        carry = math.floor(sum / 10)
        table.insert(result, 1, tostring(sum % 10))
    end

    if carry > 0 then
        table.insert(result, 1, tostring(carry))
    end

    return table.concat(result)
end

function subtractStrings(a, b)
    local aStr = tostring(a)
    local bStr = tostring(b)
    
    local maxLen = math.max(#aStr, #bStr)
    aStr = string.rep("0", maxLen - #aStr) .. aStr
    bStr = string.rep("0", maxLen - #bStr) .. bStr

    local result = {}
    local borrow = 0
    for i = maxLen, 1, -1 do
        local digitA = tonumber(aStr:sub(i, i))
        local digitB = tonumber(bStr:sub(i, i))
        local diff = digitA - digitB - borrow
        if diff < 0 then
            diff = diff + 10
            borrow = 1
        else
            borrow = 0
        end
        table.insert(result, 1, tostring(diff))
    end

    local resultStr = table.concat(result)
    resultStr = resultStr:gsub("^0+", "")

    return resultStr == "" and "0" or resultStr
end

function multiplyStrings(a, b)
    local lenA, lenB = #a, #b
    local result = "0"

    for i = lenB, 1, -1 do
        local digitB = tonumber(b:sub(i, i))
        local carry = 0
        local tempResult = {}

        for j = lenA, 1, -1 do
            local digitA = tonumber(a:sub(j, j))
            local prod = (digitA * digitB) + carry
            carry = math.floor(prod / 10)
            table.insert(tempResult, 1, tostring(prod % 10))
        end

        if carry > 0 then
            table.insert(tempResult, 1, tostring(carry))
        end

        local trailingZeros = string.rep("0", lenB - i)
        local partialResult = table.concat(tempResult) .. trailingZeros
        result = addStrings(result, partialResult)
    end

    return result
end

local INT32_MOD = "4294967296"
local function toUint32DecimalString(decValue)
    local value = tostring(decValue or "0")
    local isNegative = value:sub(1, 1) == "-"

    if isNegative then
        -- Convert signed negative decimal to uint32 decimal using two's complement.
        local absValue = value:sub(2):gsub("^0+", "")
        if absValue == "" then
            return "0"
        end
        return subtractStrings(INT32_MOD, absValue)
    end

    value = value:gsub("^0+", "")
    return value == "" and "0" or value
end

local function bytesToU32String(b1, b2, b3, b4)
    if b1 == nil or b2 == nil or b3 == nil or b4 == nil then
        return nil
    end

    if b1 < 0 then b1 = b1 + 256 end
    if b2 < 0 then b2 = b2 + 256 end
    if b3 < 0 then b3 = b3 + 256 end
    if b4 < 0 then b4 = b4 + 256 end

    local part1 = tostring(b1)
    local part2 = multiplyStrings(tostring(b2), "256")
    local part3 = multiplyStrings(tostring(b3), "65536")
    local part4 = multiplyStrings(tostring(b4), "16777216")

    local result = addStrings(part1, addStrings(part2, addStrings(part3, part4)))
    result = result:gsub("^0+", "")
    return result == "" and "0" or result, b4
end

function bytesToInt32(b1, b2, b3, b4)
    local unsigned, highByte = bytesToU32String(b1, b2, b3, b4)
    if unsigned == nil then
        return nil
    end

    if highByte >= 128 then
        return "-" .. subtractStrings(INT32_MOD, unsigned)
    end

    return unsigned
end

function bytesToUInt32(b1, b2, b3, b4)
    local unsigned = bytesToU32String(b1, b2, b3, b4)
    return unsigned
end

function decToBinaryString(decStr)
    local result = ""
    local number = decStr

    while number ~= "0" do
        local quotient, remainder = "", 0
        for i = 1, #number do
            local digit = tonumber(number:sub(i,i))
            local temp = remainder * 10 + digit
            local q = math.floor(temp / 2)
            remainder = temp % 2
            quotient = quotient .. q
        end
        result = remainder .. result
        number = quotient:match("^0*(.-)$") -- strip leading zeros
        if number == "" then 
            number = "0"
        end
    end

    -- Pad to 32 bits
    while #result < 32 do
        result = "0" .. result
    end

  return result
end

-- Extract low 28 and high 4 from binary string
function extractBits32String(decimalStr)
    local unsignedDec = toUint32DecimalString(decimalStr)
    local bin = decToBinaryString(unsignedDec)
    local high4 = tonumber(bin:sub(1, 4), 2)
    local low28 = tonumber(bin:sub(5), 2)
    return high4, low28
end

function buildBits32String(high4, low28)
    -- Convert high4 to binary string, pad to 4 bits
    local high4Bin = ""
    local h = tonumber(high4) or 0
    for i = 3, 0, -1 do
        high4Bin = high4Bin .. tostring(math.floor(h / 2^i) % 2)
    end

    -- Convert low28 to binary string, pad to 28 bits
    local low28Bin = ""
    local l = tonumber(low28) or 0
    for i = 27, 0, -1 do
        low28Bin = low28Bin .. tostring(math.floor(l / 2^i) % 2)
    end

    -- Concatenate to get full 32-bit binary string
    local binStr = high4Bin .. low28Bin

    -- Convert binary string to decimal string using string math
    local decStr = "0"
    for i = 1, #binStr do
        decStr = multiplyStrings(decStr, "2")
        if binStr:sub(i, i) == "1" then
            decStr = addStrings(decStr, "1")
        end
    end

    return decStr
end