Binary number system in Intro to Computing - Flowchart & Logic Diagram

Process Overview

The binary number system uses only two digits, 0 and 1, to represent all numbers. This flowchart shows how to convert a decimal number (like 13) into binary by repeatedly dividing by 2 and recording remainders.

Flowchart

Rectangle

↓

Rectangle

Yes No↓

Rectangle

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Rectangle

No |↓

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This flowchart shows the step-by-step process to convert a decimal number into binary by dividing by 2, recording remainders, and stopping when the number reaches zero.

Step-by-Step Trace - 15 Steps

Step 1: Input decimal number N = 13

Step 2: Check if N > 0 (13 > 0): Yes

Step 3: Record remainder 1 at front of binary digits list

Step 4: Update N = 6

Step 5: Check if N > 0 (6 > 0): Yes

Step 6: Record remainder 0 at front of binary digits list

Step 7: Update N = 3

Step 8: Check if N > 0 (3 > 0): Yes

Step 9: Record remainder 1 at front of binary digits list

Step 10: Update N = 1

Step 11: Check if N > 0 (1 > 0): Yes

Step 12: Record remainder 1 at front of binary digits list

Step 13: Update N = 0

Step 14: Check if N > 0 (0 > 0): No

Step 15: Output binary digits list as binary number: 1101

Diagram

Decimal Number (13)
     |
     v
+----------------+
| Divide by 2     |
| Quotient: 6     |
| Remainder: 1    |
+----------------+
     |
     v
+----------------+
| Divide by 2     |
| Quotient: 3     |
| Remainder: 0    |
+----------------+
     |
     v
+----------------+
| Divide by 2     |
| Quotient: 1     |
| Remainder: 1    |
+----------------+
     |
     v
+----------------+
| Divide by 2     |
| Quotient: 0     |
| Remainder: 1    |
+----------------+
     |
     v
Binary digits collected: 1 1 0 1

This diagram shows the repeated division of the decimal number 13 by 2, with the quotient and remainder at each step. The remainders collected from bottom to top form the binary number 1101.

Flowchart Quiz - 3 Questions

What is the first step in converting a decimal number to binary using this method?

A Subtract 1 from the number

B Multiply the number by 2

C Divide the number by 2 and record the remainder

D Add 1 to the number

Key Result

The binary number is formed by collecting remainders from dividing the decimal number by 2, reading them in reverse order.