CS101 - Quiz 1 Solutions

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

Convert the following unsigned binary numbers into base ten.
1. 111 = 7
2. 10110 = 22
3. 11001 = 25
4. 11111 = 31
What do all multiples of four have in common, when written in binary? (Hint: try writing the quantities 4, 8, 12, 16 in binary.)

Multiples of four always end with 00.
Convert the following 4-bit signed (two’s complement) binary numbers into base ten.
1. 0101 = +5
2. 0111 = +7
3. 1011 = –5
4. 1111 = –1
Convert the following 16-bit binary number into hexadecimal (base 16), and then into octal (base 8).
```
1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0
```
Hexadecimal: 1101,1100,1010,1110 = DCAE
Octal: 1,101,110,010,101,110 = 156256
Convert the following hexadecimal numbers into binary:
1. D1 = 1101,0001
2. F6 = 1111,0110
3. 38 = 0011,1000

Add and verify the following unsigned binary numbers.

We keep the extra carry bit, because these are unsigned and I didn’t say they were fixed width!

      1 1                        1   1             
  1 0 0 1 1 0  = 38                1 0 1 0 1 1  = 43
+   1 0 0 1 1  = 19              + 1 0 1 1 0 0  = 44
——————————————                   ——————————————
  1 1 1 0 0 1  = 57              1 0 1 0 1 1 1  = 87