[4 points for showing up]

**Using 7-bit signed (two’s complement) binary numbers, what is the largest positive number? What is the smallest negative number?**[6 points]In 7-bit two’s complement, the column values are:

`___ ___ ___ ___ ___ ___ ___ -64 32 16 8 4 2 1`

So the largest positive number is 0111111 = 63 and the most negative number is 1000000 = -64.

**Convert the following 16-bit binary number into hexadecimal.**[6 points]`8 4 2 1 8 4 2 1 8 4 2 1 8 4 2 1 ------- ------- ------- ------- 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 0 7 F 3 A`

**Add and verify the following unsigned binary numbers.**[6 points]`1 1 1 1 1 1 1 1 0 1 1 1 1 = 47 1 1 0 1 1 1 = 55 + 0 1 1 1 0 1 = 29 + 1 0 0 1 0 0 = 36 -------------- -- -------------- -- 1 0 0 1 1 0 0 = 76 1 0 1 1 0 1 1 = 91 32 8 2 32 8 2 64 16 4 1 64 16 4 1`

**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?**[6 points]We need 4 bits per character, which allows 16 distinct characters to be represented.

**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.**[6 points]`T 00 R 010 N 011 O 1`

**Use the character encoding from the previous question to decode the following word:**[6 points]`0 0,1,0 1 0,1,0 1 1,0 0,1 T O R O N T O`