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Or, more generally, you can chain an arbitrary series of adders to form an N-bit adder. First you define an abbreviation for the AndL function to represent the composition of multiple circuit blocks: let Blocks l = AndL l And here is the definition of an N-bit adder with a halfAdder at one end: let nBitCarryRippleAdder (n:int) (x:bitvec) (y:bitvec) (sum:bitvec) (carry:bitvec) = Blocks [ for i in 0 .. n-1 -> if i = 0 then halfAdder x.[i] y.[i] sum.[i] carry.[i] else fullAdder x.[i] y.[i] carry.[i-1] sum.[i] carry.[i] ] Using a similar approach, you get the following satisfying specification of a symmetric N-bit adder that accepts a carry as input and also gives a carry as output: let rippleAdder (n:int) (x:bitvec) (y:bitvec) (sum:bitvec) (carry:bitvec) Blocks [ for i in 0 .. n-1 -> fullAdder x.[i] y.[i] carry.[i] sum.[i] carry.[i+1] ] =

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So, OS authentication won t work and, as discussed earlier, if you re trying to start up an instance to mount and open a database, then by definition there s no database yet in which to look up authentication details It is the proverbial chicken and egg problem Enter the password file The password file stores a list of usernames and passwords that are allowed to remotely authenticate as SYSDBA over the network Oracle must use this file to authenticate them, not the normal list of passwords stored in the database So, let s correct our situation First, we ll start up the database locally so we can set the REMOTE_LOGIN_PASSWORDFILE Its default value is NONE, meaning there is no password file; there are no remote SYSDBA logins.

It has two other settings: SHARED (more than one database can use the same password file) and EXCLUSIVE (only one database uses a given password file) We ll set ours to EXCLUSIVE, as we want to use it for only one database (ie, the normal use): sys%ORA11GR2> alter system set remote_login_passwordfile=exclusive scope=spfile; System altered This setting can t be changed dynamically while the instance is up and running, so we ll have to shut down and this will take effect upon the next restart.

Let s now take a look at the propositional formula for a halfAdder with variable inputs and outputs: > halfAdder (var "x") (var "y") (var "sum") (var "carry");; > val it : Prop = And(Not And (Not And (Var "sum", Not Not And (Not And (Var "x",Var "y"),Not And (Not Var "x",Not Var "y"))), Not And (Not Var "sum", Not Not Not And (Not And (Var "x",Var "y"),Not And (Not Var "x",Not Var "y")))), Not And (Not And (Var "carry",And (Var "x",Var "y")), Not And (Not Var "carry",Not And (Var "x",Var "y")))) Clearly, you don t want to be doing too much of that! You will see better ways of inspecting circuits and the symbolic values of bit vectors in the section Representing Propositional Formulae Efficiently Using BDDs.

The next step is to use the command-line tool (on UNIX and Windows) named orapwd to create and populate the initial password file: $ orapwd Usage: orapwd file=<fname> entries=<users> force=<y/n> ignorecase=<y/n> nosysdba=<y/n> where file is the name of password file (required); password is the password for SYS; it will be prompted if not specified at command line; entries are the maximum number of distinct DBAs (optional); All rights reserved..

In passing, we note that the twoBitAdder uses an internal wire. You could model this using an existential formula: let twoBitAdderWithHiding (x1,x2) (y1,y2) (sum1,sum2) carry = let carryInnerVar = fresh "carry" let carryInner = var(carryInnerVar) Exists(carryInnerVar, halfAdder x1 y1 sum1 carryInner &&& fullAdder x2 y2 carryInner sum2 carry) However, this brings up issues beyond the scope of this chapter, and instead we take an approach to modeling where there are no boundaries to the circuits and where all internal wires are exposed.