While-loop flow chart Decimal to binary representations

Lecture 6 While-Loop programming

While loopstatementsfalsewhile entry_condition statements;endECend

Flow chartstatementsfalse Execute body statements repeatedly until the entry condition fails The entry condition should eventually become false by iteratively executing body statementsECend

Decimal to binary representationsInput : positive decimal numbersOutput : binary representations of the input

Modulus: find remainder >> rm=mod(10,3)

ans =

1>> rm=mod(100,7)

ans =

2

Quotient>> quo=floor(100/7)

ans =

14>> quo=floor(10/3)

ans =

3

Decimal to binary representationLet M be a positive decimal numberLet b be an array of length n

b denotes the binary representation of M if

ExampleM > 0M=1, b1=1M=5, 101C=101

Example

M=25, C: 11001

The problem is to find b for given M11001

ExampleM > 0M=1, b1=1M=5, b=[1 0 1]M=25, b=[1 1 0 0 1]The problem is to find b for given M

Decimal to binary representationGiven M>0, find array bStrategy : Iteratively find b1 ,b2 ,,bnAppend from left to b

Find b1 r = mod(q,2);q_new = (q-r)/2;

remainder

Find b2 r = mod(q,2);q_new = (q-r)/2;Append remainder from left-hand-side

Find bi r = mod(q,2);q_new = (q-r)/2;Append remainder from left-hand-side

An iterative approachq=M; b=[];Calculate r, qnew and bi iterativelyAppend bi to b from left-hand-side q qnewuntil q equal zeroreturn b

StrategystatementstrueECendq=M; b=[];Calculate r, qnew and bi iterativelyAppend bi to b from left-hand-sideq qnewuntil q equal zeroreturn b

An iterative approachq=M; b=[];Calculate r, qnew and bi iterativelyAppend bi to b from left-hand-sideq qnewuntil q equal zeroreturn b Calculate r, qnew and bi Append bi to b from left-hand-sideq qnewtrueq>0endq=M; b=[]

An iterative approachCalculate rAppend r to b from left-hand-sideUpdate qq=M; b=[];Calculate r, qnew and bi iterativelyAppend bi to b from left-hand-sideq qnewuntil q equal zeroreturn b trueq>0endq=M; b=[]

Entry conditionEntry condition

q > 0Halt if q==0

Determine b

Change base

Decimal to Octal representation

>> dec2oct(7)

ans =

7

>> dec2oct(8)

ans =

1 0

>> dec2oct(18)

ans =

2 2

>> dec2oct(64)

ans =

1 0 0