To convert the decimal number 76 into an 8-bit binary representation, follow these steps:
### Step 1: Divide the Number by 2
Start by dividing 76 by 2 and record the quotient and the remainder. The remainder will be part of the binary representation.
1. **76 ÷ 2 = 38**, remainder **0**
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**
### Step 2: Collect the Remainders
Now, write down the remainders from the last division to the first:
- The remainders are: **1, 0, 0, 1, 1, 0, 0, 0**
### Step 3: Write in Reverse Order
To get the binary number, reverse the order of the remainders:
- Reading from bottom to top: **1001100**
### Step 4: Format as 8-Bit Binary
Since we need an 8-bit binary representation, we can add leading zeros to ensure it has 8 digits:
- The 8-bit representation of 76 is **01001100**.
### Summary
The decimal number 76 in 8-bit binary is **01001100**. This format is useful in various computing applications where binary data representation is required, such as in programming, digital electronics, and data encoding.