Perform the following binary additions. Interpret the numbers as 8-bit unsigned

Question

Perform the following binary additions. Interpret the numbers as 8-bit unsigned integers, translate them to decimal, check if the result is within the valid range, and show how to verify a possible overflow condition in the binary addition algorithm. Then follow these same steps by interpreting the numbers as 8-bit signed integers instead. Perform the following binary multiplications using a 7-bit unsigned representation. Convert the numbers to decimal, and verify the correct result of the operation.

Explanation / Answer

6

8 bit unsigned integers

11110001

+ 100010

---------------

1)00010011

------------------

There is overflow condition as the number of bits are 8 and allowed range is between 00000000(0 in decimal) and 11111111(255)

241 + 34 = 275

275 >255 so 275 cannot be accomodated in 8 bits

1111000

+ 1010

------------

10000010

----------------

120 +10 = 130

130<255 so 130 can be accomodated in 8 bits, there is no overflow condition.

8 bit signed integers

1 1110001

1 00010

+

------------------

1 1110011

-----------------

leftmost bit is sign bit so is not used for addition, both numbers are negative as sign bit is 1

-113 + (-2) = - 115

range is -127 to 128

so can ne accomodated in 8 bits

1 111000

1 010

+

----------------

1 111010

------------

-56 +(-2) = -58

It is also in range

7

10110

* 101

----------

10110

00000*

10110**

-------------

1101110

------------

22 * 5 = 110

so answer is correct and can be done in 7 bits as range of values in 7 bits is between 0000000(0 in decimal) and 1111111(127)

110<127 so can be done.

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