Assignment

1) What is the base-10 equivalent of:

1.a) 1011, a 4-bit two's complement number
2.b) 1111, a 4-bit one's complement number
3.c) FEB2FEFE hexadecimal (unsigned integer)

2) What are the differences between using single precision vs. double precision floating point numbers in how numbers (size, accuracy, etc.) can be represented?

3) Describe the conditions that have to be in place for an overflow to occur after an integer addition operation.

• When adding two numbers, overflow occurs when the two operands have the same leftmost bit and the leftmost bit of the answer is different.

• When the operands have differing leftmost bits, overflow cannot occur when adding them together because we are adding a positive number with a negative number which means we are actually subtracting. It implies that the result cannot be bigger than the operands.

So, there is no possibility of overflow in this case. The leftmost bit is frequently referred to as the Most Significant Bit (MSB for short).

Problem

4) Add the following 16-bit 2's complement numbers (represented in Hex): 78BF + FAA4 and indicate whether or not there is a carry and/or an overflow generated. Also, if no overflow, give the result in base-10 format.

5) Add the following 16-bit 2's complement numbers (represented in Hex): 8FE8 + 82BF and indicate whether or not there is a carry and/or an overflow generated. Also, if no overflow, give the result in base-10 format.

6) If the term excess-128 notation is used in context of an exponent that is 8-bits in length, what is the range of the power that the exponent can represent?

7) Using the floating-point format, convert the binary number -101011101010.101011011 to the floating-point representation.

8) Using the floating-point format, convert the floating-point number represented by 2FFCEE40 to base 10 (decimal) representation.

9) Provide a hexadecimal ASCII conversion for the following text phrase: I like to watch TV at 9:30.