# Homework 9

### Appendix A

1. Convert the following numbers to binary: 1984, 4000, 8192.

2. What is 1001101001 (binary) in decimal? In octal? In hexadecimal?

4. How many different positive integers can be expressed in k digits using radix r numbers?

5. Perform the following calculations on 8-bit two’s complement numbers. What are the values of each number, and each result, in base 10?

```  00101101   11111111   00000000   11110111
+ 01101111 + 11111111 + 11111111 + 11110111
```

6. How do you add and subtract two numbers in 2's compliment? Convert the following problems into 8-bit 2's complement numbers, do them in binary, and convert back. Show your work.

• 23 + 12 = ?
• 42 - 16 = ?
• 17 - 32 = ?
• -15 + -32 = ?
7. What happens when you try to add the following numbers if represented in two's complement 8-bit numbers? Show the results in binary, and explain the problem:

• 65+82 = ?
• -76+ -88 = ?
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Topic revision: r2 - 2014-10-12 - JimSkon

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