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Lecture Topic: Computer Number Systems in Break 1. Convakowt Grorpp: the following decimal numbers (Base 10) into binary format (Base 2) a. 77 b. 1144 c. 234

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Feb 03,2025

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**Conversions of Decimal to Binary:** - **77** in binary is **1001101₂** - **1144** in binary is **10001111000₂** - **234** in binary is **11101010₂** **Summary:** | Decimal | Binary | |---------|--------------| | 77 | 1001101₂ | | 1144 | 10001111000₂ | | 234 | 11101010₂ | If you need more examples or further assistance, feel free to ask!

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### Lecture Topic: Computer Number Systems #### **1. Convert the following decimal numbers (Base 10) into binary format (Base 2)** --- ##### **a. 77** **Conversion Steps:** To convert the decimal number **77** to binary, divide the number by 2 repeatedly and record the remainders. | Division Step | Quotient | Remainder | |---------------|----------|-----------| | 77 ÷ 2 | 38 | 1 | | 38 ÷ 2 | 19 | 0 | | 19 ÷ 2 | 9 | 1 | | 9 ÷ 2 | 4 | 1 | | 4 ÷ 2 | 2 | 0 | | 2 ÷ 2 | 1 | 0 | | 1 ÷ 2 | 0 | 1 | **Binary Representation:** Read the remainders from bottom to top: `1 0 0 1 1 0 1` So, **77** in binary is: **`1001101₂`** --- ##### **b. 1144** **Conversion Steps:** To convert the decimal number **1144** to binary, divide the number by 2 repeatedly and record the remainders. | Division Step | Quotient | Remainder | |---------------|----------|-----------| | 1144 ÷ 2 | 572 | 0 | | 572 ÷ 2 | 286 | 0 | | 286 ÷ 2 | 143 | 0 | | 143 ÷ 2 | 71 | 1 | | 71 ÷ 2 | 35 | 1 | | 35 ÷ 2 | 17 | 1 | | 17 ÷ 2 | 8 | 1 | | 8 ÷ 2 | 4 | 0 | | 4 ÷ 2 | 2 | 0 | | 2 ÷ 2 | 1 | 0 | | 1 ÷ 2 | 0 | 1 | **Binary Representation:** Read the remainders from bottom to top: `1 0 0 0 0 1 1 1 1 0 0 0` So, **1144** in binary is: **`10001111000₂`** --- ##### **c. 234** **Conversion Steps:** To convert the decimal number **234** to binary, divide the number by 2 repeatedly and record the remainders. | Division Step | Quotient | Remainder | |---------------|----------|-----------| | 234 ÷ 2 | 117 | 0 | | 117 ÷ 2 | 58 | 1 | | 58 ÷ 2 | 29 | 0 | | 29 ÷ 2 | 14 | 1 | | 14 ÷ 2 | 7 | 0 | | 7 ÷ 2 | 3 | 1 | | 3 ÷ 2 | 1 | 1 | | 1 ÷ 2 | 0 | 1 | **Binary Representation:** Read the remainders from bottom to top: `1 1 0 1 0 1 0` So, **234** in binary is: **`11101010₂`** --- ### **Summary of Conversions** | Decimal | Binary | |---------|--------------| | 77 | 1001101₂ | | 1144 | 10001111000₂ | | 234 | 11101010₂ | --- ### **Additional Explanation** **Methodology for Conversion:** 1. **Divide the Decimal Number by 2:** - Perform integer division of the number by 2. - Record the remainder (either 0 or 1). 2. **Repeat the Process:** - Use the quotient obtained from the previous division as the new number to divide by 2. - Continue this process until the quotient is 0. 3. **Construct the Binary Number:** - The binary number is formed by collecting all the remainders in reverse order (from last to first). **Example: Converting 77 to Binary** 1. 77 ÷ 2 = 38 remainder **1** 2. 38 ÷ 2 = 19 remainder **0** 3. 19 ÷ 2 = 9 remainder **1** 4. 9 ÷ 2 = 4 remainder **1** 5. 4 ÷ 2 = 2 remainder **0** 6. 2 ÷ 2 = 1 remainder **0** 7. 1 ÷ 2 = 0 remainder **1** Reading the remainders from bottom to top: **1001101** Therefore, **77** in binary is **`1001101₂`**. --- If you have any further questions or need more examples, feel free to ask!

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Mind Expander

To convert the decimal numbers to binary, one fun way is to keep dividing the number by 2 and writing down the remainders! For 77, you would divide it by 2 repeatedly until you hit 0, and you get the binary representation as 1001101. For 1144, that process yields 10001110000, and for 234, you'll end up with 11101010. It's a bit like a treasure hunt for binary digits! Want to impress your friends with this skill? You can always practice with larger decimal numbers! After mastering the basic numbers, tackle some challenges, like converting your age or the number of steps you take in a day. You'll be the binary guru in no time, and who knows, it might come in handy someday during a geeky trivia night!

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