# 5 Problems with Data Representation Formats, MIPS Instructions, and Assembly

Subject Computer Science Systems Architecture

## Question

Question 1
Binary numbers can be interpreted in a number of ways. Consider the following 32-bit binary number:
0010 0000 1011 0100 0000 0000 1001 0100
a) What is the value when interpreted as a set of four 8-bit 2's complement signed integers?

Question 2:
The MIPS branch instructions modify the program counter (PC) by adding an immediate two's complement value.
a) What does this value represent?
b) Why is this value multiplied by 4 before being added to the program counter?

Question 3:
Find one of each of the following types of devices, either in your house, at work, or elsewhere. For each device that you find, try to discover the CPU chip manufacturer and assembly language of the main processor, as well as the processing speed, ram, and L1 cache amounts

- Embedded special-purpose computer such as a digital camera, smart refrigerator, or car navigation system.

Question 4:
Describe, in your own words, the difference(s) between the following concepts:
- Overflow versus carry out
- truncation error versus rounding error
- two’s complement representation versus biased representation (used in IEEE 754 floating point)
- NaN versus infinity
- Machine language versus assembly language

Question 5:
Represent each of the following values in the IEEE 754 32-bit format, truncating inexact values. Indicate the percent error of the value stored compared to the exact value. This will require you to convert the 32 bit floating point number back to decimal and compare to the original value.
a) -37 1/4
b) +12 1/5

## Solution Preview

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2a) The target address is the offset (immediate operand) from incremented PC old value. It is used the 2’s complement value because this shows if the target address resides forward or backward compared to the old PC value. By default, in MIPS the offset value is equal with number of words minus 1. The explanation also resides in the fact that branch instructions use PC-relative addressing mode and not absolute....

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