```plantuml
@startuml
title Exchange Connection Logic Flow

start

:User Lands on Client Page;

if ("Is User New?") then (Yes)
    :Attempt to Connect to Default Exchange (Public-Only);
    if ("Default Exchange Supports Public Connection?") then (Yes)
        :Connect Default Exchange in Public-Only Mode;
        note right: Scenario A
    else (No)
        :Failed to Connect Default Exchange;
        stop
    endif
else (No)
    :Retrieve Previously Connected Exchanges and Modes;
    :Reconnect to Default Exchange based on Previous Mode;
endif

:User Chooses to Connect an Exchange;

if ("Exchange is Already Connected?") then (Yes)
    if ("User Provides New API Keys?") then (Yes)
        :Compare New API Keys with Existing Ones;
        if ("Keys Differ?") then (Yes)
            :Update API Keys in Database;
            :Re-instantiate Exchange Object with New Keys;
            :Attempt Authentication;
            if ("Authentication Successful?") then (Yes)
                :Status = api_keys_updated;
                note right: Scenarios C, F, G
            else (No)
                :Status = failure;
                note right: Scenarios E
            endif
        else (No)
            :Status = already_connected;
            note right: Scenario D
        endif
    else (No)
        :Check Current Connection Mode;
        if ("Currently in Authenticated Mode?") then (Yes)
            :Status = already_connected;
        else (No)
            :Status = connected_public_only;
            note right: Scenarios B, D
        endif
    endif
else (No)
    :User Provides API Keys?;
    if ("Exchange Requires API Keys?") then (Yes)
        if ("API Keys Provided?") then (Yes)
            :Attempt to Connect and Authenticate Exchange;
            if ("Authentication Successful?") then (Yes)
                :Status = success;
                note right: Scenarios C, F
            else (No)
                :Status = failure;
                note right: Scenario E
            endif
        else (No)
            :Alert User to Provide API Keys;
            stop
        endif
    else (No)
        :Attempt to Connect to Exchange in Public-Only Mode;
        if ("Connection Successful?") then (Yes)
            :Status = connected_public_only;
            note right: Scenarios B
        else (No)
            :Status = failure;
            note right: Scenario B
        endif
    endif
endif

:Return Status to Client;

if ("Status = success or api_keys_updated") then (Yes)
    :Client Reloads Page to Reflect Changes;
else (No)
    if ("Status = connected_public_only or already_connected") then (Yes)
        :Client Shows Informational Message;
    else (No)
        :Client Shows Error Message;
    endif
endif

stop

@enduml

```