# Quiz 1 Solutions

Mon Sep 17

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

1. Suppose we have the digits 265, written using base seven. What quantity does that represent, expressed in base ten?

The column values in base seven are (left to right) 49, 7, and 1. So the value 265 represents 2×49 + 6×7 + 5×1 = 98 + 42 + 5 = 145.

2. Convert the following unsigned binary numbers into base ten.

1. 11100      = 28
2.   111      =  7
3. 11010      = 26
4. 10101      = 21
3. Convert the following base ten numbers into binary, using as many bits as needed.

1. 12      =   1100
2. 17      =  10001
3. 31      =  11111
4. 40      = 101000
4. When using fixed-width 4-bit unsigned binary numbers, what is 13 + 7? (Convert those to 4-bit binary, add the bits to get a 4-bit answer, and convert back to base ten.)

13+7 in base ten is 1101+0111 in binary. That results in 0100 with an extra carry that we throw away. So 13+7=4.

5. Convert the following signed numbers into binary using 6-bit signed two’s complement. (Every answer should include all six bits.)

1.  -1      = 111111
2. -17      = 101111
3.  27      = 011011
4. -32      = 100000
B9E5 =
 B9E5 = 1011 1001 1110 0101