# Quiz 1 Solutions

Mon Feb 2

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

1. Suppose we have the digits 152, written using base six. What quantity does that represent, expressed in base ten? +2

The column values in base six are (left to right) 36, 6, and 1. So this number is 1×36 + 5×6 + 2×1 = 36 + 30 + 2 = 68.

2. Convert the following unsigned binary numbers into base ten. +4

1. 11100    = 28
2. 11011    = 27
3. 11001    = 25
4. 111    = 7
3. Convert the following base ten numbers into binary using 5-bit signed two’s complement +4

1. $$-12$$    = 10100
2. $$13$$    = 01101
3. $$-8$$    = 11000
4. $$-1$$    = 11111
4. Add and verify the following unsigned (not fixed-size) binary numbers. +4

We keep the extra carry bit, because these are not fixed width!

    1 1                          1 1 1 1
1 1 0 0  = 12                  1 1 1 1 1  = 31
+ 1 0 0 1 1 0  = 38              + 1 0 0 1 0 0  = 36
——————————————                   ——————————————
1 1 0 0 1 0  = 50              1 0 0 0 0 1 1  = 67
5. Convert the hexadecimal number 27C to binary. +3

0010 0111 1100

6. Convert the octal number 615 to binary. +3

110 001 101