Quiz 1

PDF version

You have up to 25 minutes. You may use a calculator, but no text book or notes.

Using 7-bit signed (two’s complement) binary numbers, what is the largest positive number? What is the smallest negative number?
Convert the following 16-bit binary number into hexadecimal.
```
0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0
```

Add and verify the following unsigned binary numbers.

  1 0 1 1 1 1                      1 1 0 1 1 1
+ 0 1 1 1 0 1                    + 1 0 0 1 0 0
——————————————                   ——————————————

Suppose we need to send a text message uses just 15 distinct characters. How many bits per character are required if we’re using a fixed encoding?
Draw a binary tree that corresponds to the following variable-width encoding of four characters. The characters should appear in boxes at the leaves. Branch left on a zero, or right on a one.
```
T 00  
R 010 
N 011 
O 1   
```
Use the character encoding from the previous question to decode the following word:
```
0 0 1 0 1 0 1 0 1 1 0 0 1
```