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.

Practice

1. What digits are used in the binary number system?

easy

A. Digits 1 to 10

B. Digits 0 to 9

C. Digits 0 to 7

D. Only 0 and 1

Solution

1. Step 1: Understand the binary system basics

   The binary number system uses only two digits to represent all numbers.

2. Step 2: Identify the digits used

   These digits are 0 and 1, representing off and on states in computers.

3. Final Answer:

   Only 0 and 1 -> Option D

4. Quick Check:

   Binary digits = 0 and 1 [OK]

Hint: Binary uses just two digits: 0 and 1 [OK]

Common Mistakes:

• Confusing binary with decimal digits
• Thinking binary uses digits 0 to 9
• Assuming binary includes digits beyond 1

2. Which of the following is the correct binary number?

easy

A. 1101

B. 1234

C. 1021

D. 2010

Solution

1. Step 1: Check each digit for binary validity

   Binary numbers only contain 0s and 1s. Check each option's digits.

2. Step 2: Identify the valid binary number

   1101 is 1101, which contains only 1s and 0s. Others have digits like 2 or 3, invalid in binary.

3. Final Answer:

   1101 -> Option A

4. Quick Check:

   Valid binary = digits 0 or 1 only [OK]

Hint: Binary digits are only 0 or 1, no other digits allowed [OK]

Common Mistakes:

• Choosing numbers with digits other than 0 or 1
• Confusing binary with decimal or octal numbers
• Ignoring invalid digits in options

3. What is the decimal value of the binary number 1011?

medium

A. 7

B. 11

C. 13

D. 9

Solution

1. Step 1: Assign powers of 2 to each bit

   From right to left, bits represent 2^0=1, 2^1=2, 2^2=4, 2^3=8.

2. Step 2: Calculate decimal value by adding bits with 1

   Bits: 1(8) + 0(4) + 1(2) + 1(1) = 8 + 0 + 2 + 1 = 11.

3. Final Answer:

   11 -> Option B

4. Quick Check:

   Binary 1011 = Decimal 11 [OK]

Hint: Add powers of 2 where bit is 1, starting from right [OK]

Common Mistakes:

• Misaligning bit positions and powers of 2
• Adding all bits instead of weighted values
• Confusing binary digits with decimal digits

4. Identify the error in this binary number: 11012

medium

A. Binary numbers cannot start with 1

B. Too many digits for a binary number

C. Contains digit '2' which is invalid in binary

D. Missing leading zeros

Solution

1. Step 1: Check each digit for binary validity

   Binary digits must be only 0 or 1. The digit '2' is not allowed.

2. Step 2: Confirm the invalid digit

   The presence of '2' makes the number invalid as a binary number.

3. Final Answer:

   Contains digit '2' which is invalid in binary -> Option C

4. Quick Check:

   Binary digits = 0 or 1 only [OK]

Hint: Binary digits never include 2 or higher [OK]

Common Mistakes:

• Thinking binary numbers have digit limits on length
• Believing binary cannot start with 1
• Assuming missing zeros is an error

5. Convert the decimal number 18 to binary.

hard

A. 10010

B. 11001

C. 10110

D. 10001

Solution

1. Step 1: Divide decimal number by 2 repeatedly

   18 ÷ 2 = 9 remainder 0; 9 ÷ 2 = 4 remainder 1; 4 ÷ 2 = 2 remainder 0; 2 ÷ 2 = 1 remainder 0; 1 ÷ 2 = 0 remainder 1.

2. Step 2: Write remainders in reverse order

   Reading remainders from last to first: 1 0 0 1 0.

3. Final Answer:

   10010 -> Option A

4. Quick Check:

   Decimal 18 = Binary 10010 [OK]

Hint: Divide by 2, collect remainders backward [OK]

Common Mistakes:

• Reading remainders in wrong order
• Mixing up division and subtraction steps
• Confusing binary digits with decimal digits