Mon Sep 17

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

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.

Convert the following

**unsigned**binary numbers into base ten.`11100`

=`28`

`111`

=`7`

`11010`

=`26`

`10101`

=`21`

Convert the following base ten numbers into binary, using as many bits as needed.

`12`

=`1100`

`17`

=`10001`

`31`

=`11111`

`40`

=`101000`

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`

.Convert the following signed numbers into binary using

**6-bit signed two’s complement.**(Every answer should include all six bits.)`-1`

=`111111`

`-17`

=`101111`

`27`

=`011011`

`-32`

=`100000`

Convert the following

**hexadecimal**(base 16) number to**binary.**(Your answer should contain 16 bits.)`B9E5 =`

`B9E5 = 1011 1001 1110 0101`