In an 8-bit two’s complement system, negative numbers are represented by inverting all the bits of the positive version of the number (i.e., taking the one's complement) and then adding 1 to the result.

Let's find the 8-bit two's complement representation of -60:

### Step 1: Represent +60 in binary
The binary representation of +60 in 8 bits is:
```
+60 = 0011 1100
```

### Step 2: Find the one’s complement
To find the one's complement, invert each bit:
```
One’s complement of 0011 1100 = 1100 0011
```

### Step 3: Add 1 to the one’s complement
Now, add 1 to the one's complement to get the two's complement:
```
1100 0011
+        1
------------
1100 0100
```

Thus, the 8-bit two's complement representation of -60 is:
```
1100 0100
```

Would you like more details or have any other questions?

Here are five related questions to consider:
1. How is overflow handled in two's complement arithmetic?
2. What is the two's complement of -128 in an 8-bit system?
3. How does sign extension work when converting 8-bit two’s complement to 16-bit?
4. What is the largest positive number that can be represented in 8-bit two’s complement?
5. How would you represent -1 in an 8-bit two's complement system?

**Tip:** In two's complement, the leftmost bit (most significant bit) represents the sign of the number. A '1' indicates a negative number, and a '0' indicates a positive number.

Learn how to convert -60 into its 8-bit two's complement binary representation with a step-by-step guide. This solution explains key concepts such as one's complement, two's complement, and binary arithmetic. Perfect for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation