Activity - 2 Number System Conversion - Class VII

Number System Conversion Helper

Learn to convert between Binary, Octal, and Hexadecimal using simple lookup tables!

Octal ↔ Binary Conversion

Conversion Table: Octal ↔ Binary (3-bit groups)

Octal	Binary (3-bit)
0	000
1	001
2	010
3	011
4	100
5	101
6	110
7	111

Steps for Octal to Binary Conversion

1. **Step 1: Identify Each Octal Digit.** Look at the octal number you want to convert.
2. **Step 2: Lookup in Table.** For each octal digit, find its corresponding 3-bit binary equivalent in the table above.
3. **Step 3: Concatenate.** Join all the 3-bit binary groups together in the same order to form the final binary number.

Example: Convert Octal 257₈ to Binary

Octal Number: 257₈

• Digit 2 → 010₂ (from table)
• Digit 5 → 101₂ (from table)
• Digit 7 → 111₂ (from table)

Concatenate: 010101111₂

Therefore, 257₈ = 010101111₂

Steps for Binary to Octal Conversion

1. **Step 1: Group Binary Digits.** Starting from the **rightmost** digit of the binary number, group the digits into sets of three.
2. **Step 2: Pad with Zeros (if needed).** If the leftmost group has fewer than three digits, add leading zeros until it has three digits.
3. **Step 3: Lookup in Table.** For each 3-bit group, find its corresponding octal digit in the table.
4. **Step 4: Concatenate.** Join all the octal digits together in the same order to form the final octal number.

Example: Convert Binary 1101001₂ to Octal

Binary Number: 1101001₂

• Group from right: 1 101 001
• Pad leftmost group: 001 101 001
• 001₂ → 1₈ (from table)
• 101₂ → 5₈ (from table)
• 001₂ → 1₈ (from table)

Concatenate: 151₈

Therefore, 1101001₂ = 151₈

Hexadecimal ↔ Binary Conversion

Conversion Table: Hexadecimal ↔ Binary (4-bit groups)

Hex	Binary (4-bit)
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001
A	1010
B	1011
C	1100
D	1101
E	1110
F	1111

Steps for Hexadecimal to Binary Conversion

1. **Step 1: Identify Each Hexadecimal Digit.** Look at the hexadecimal number you want to convert.
2. **Step 2: Lookup in Table.** For each hexadecimal digit, find its corresponding 4-bit binary equivalent in the table above.
3. **Step 3: Concatenate.** Join all the 4-bit binary groups together in the same order to form the final binary number.

Example: Convert Hexadecimal A3F₁₆ to Binary

Hexadecimal Number: A3F₁₆

• Digit A → 1010₂ (from table)
• Digit 3 → 0011₂ (from table)
• Digit F → 1111₂ (from table)

Concatenate: 101000111111₂

Therefore, A3F₁₆ = 101000111111₂

Steps for Binary to Hexadecimal Conversion

1. **Step 1: Group Binary Digits.** Starting from the **rightmost** digit of the binary number, group the digits into sets of four.
2. **Step 2: Pad with Zeros (if needed).** If the leftmost group has fewer than four digits, add leading zeros until it has four digits.
3. **Step 3: Lookup in Table.** For each 4-bit group, find its corresponding hexadecimal digit in the table.
4. **Step 4: Concatenate.** Join all the hexadecimal digits together in the same order to form the final hexadecimal number.

Example: Convert Binary 1110101100₂ to Hexadecimal

Binary Number: 1110101100₂

• Group from right: 11 1010 1100
• Pad leftmost group: 0011 1010 1100
• 0011₂ → 3₁₆ (from table)
• 1010₂ → A₁₆ (from table)
• 1100₂ → C₁₆ (from table)

Concatenate: 3AC₁₆

Therefore, 1110101100₂ = 3AC₁₆

Try it Yourself! (Interactive Converter)

Enter Number: Octal Binary Hexadecimal

Binary:

Octal:

Hexadecimal:

Conversion Steps:

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