Assignment #2
Lyndsay Clark
Study.com
Computer Science 306: Computer Architecture
February 19, 2026
Assignment #2
Part 1:
1. Hex: 130F204B3C, Dec: 81858153276
2. F1552FA3
3. 563274
4. .
Binary
Octal
000
0
001
1
010
2
011
3
100
4
101
5
110
6
111
7
1000
10
1001
11
1010
12
1011
13
1100
14
1101
15
1110
16
1111
17
10000
20
Decimal
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Hexadecimal
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
10
Part 2:
NAND
X = (A · B)′
A
0
0
1
1
B
0
1
0
1
X
1
1
1
0
NOR
X = (A + B)′
A
0
0
1
1
B
0
1
0
1
X
1
0
0
0
XOR
X = A ⊕ B = A′B + AB′
A
0
0
1
1
B
X
0
1
0
1
0
1
1
0
NOT
X = A′
A
X
0
1
3-Input AND
X=A·B·C
A
0
0
0
0
1
1
1
1
1
0
B
0
0
1
1
0
0
1
1
C
0
1
0
1
0
1
0
1
X
0
0
0
0
0
0
0
1
Part 3:
Fixed-point numbers use a fixed position for the binary point. This is so values can be stored as
scalable integers. This might seem like a small technical detail, but it actually makes a different in most
systems. A lot of embedded processors operate under tight limits on memory, speed, and power. Many
of these chips do not include efficient floating-point hardware. In those environments, fixed-point
arithmetic runs faster and consumes less energy, which makes it the practical choice.
It is important to study fixed-point manipulation because the scale is a real,practical design
decision. One chooses how many bits represent the integer portion and how many represent the
fractional portion. That choice determines your precision in the range of values. If you choose badly,
values can overflow or important detail can be lost. You also need clear rules for rounding, saturation, or
wraparound. Those decisions directly affect how the system behaves in real use.
Fixed-point arithmetic is necessary to meet strict timing requirements in real-time systems.
Control loops must execute within fixed deadlines to maintain safe and correct operation. In motor
control systems, for example, a controller may be required to update a PWM signal every few
microseconds. If the computation does not complete before the next update cycle, the system can fail
to respond correctly. Fixed-point operations rely on basic integer instructions such as addition,
subtraction, shifting, and multiplication. These operations are simple to implement in hardware and are
easier to schedule in software than floating-point operations. As a result, execution time is more
predictable and stable. This makes it so that predictable timing is critical in real-time control systems.
Fixed-point study is also relevant for signal processing. Audio, speech, and sensor filters run on
low-cost DSP chips. These systems use many multiply and accumulate steps. Word length affects noise
and stability. When learning, one can start with floating-point models, then they convert to fixed-point
code for the target chip. This conversion is a standard step in DSP work (Gan & Kuo, 2006). If you do not
properly scale, the filter can clip or drift.
Another reason for this is safety. Fixed-point can be predictable. Floating-point has rules too,
but it can cause errors or raise exceptions and it can behave differently with different settings. The IEEE
floating-point standard is what defines the formats, the rounding, and the exception behavior for
floating-point operations (ISO/IEC/IEEE, 2011). Fixed-point avoids many of those cases with the use of
integer hardware and also the use of explicit scaling. For many embedded products, predictability is
more important than the dynamic range.
You also see fixed-point inside sensors and data links. Many sensors output values in a Q
format. The bits represent a scaled value, not a pure integer. If you misread the scale, you get wrong
units. Texas Instruments explains Q format. Fixed-point data always has a chosen resolution (Texas
Instruments, 2024). Learning this allows us to decode devices in real world applications.
Fixed-point also helps when you need repeatable results. A game replay, for instance, should
match on two devices. A robotics log should match after a firmware update. With fixed-point, you
control every shift and every rounding step. You can also prove bounds more easily. This makes the
largest sum calculable and demonstrable. You can show the smallest possible step. That helps during
testing. That also helps in reviews. It supports clear requirements. T
Fixed-point is common in phones and cars. Audio codecs use fixed-point steps to save power.
Cameras use fixed-point for image filters and color math. Cars use fixed-point in engine control and
battery management. Drones use it for attitude estimation. Medical devices use it for low-power signal
processing. Routers use it for rate control and timers. Finance systems also use scaled integers for cents
in thie numerical calculations to avoid rounding surprises.
Studying fixed-point manipulation teaches us good habits. You learn to track units. You learn to
bound values. You learn to test extremes. You learn to design with bit budgets. These skills transfer to
CPU design, ALU design, and assembly work. They also match real limits in hardware. Fixed-point is not
old. It is a practical tool that shows up every day.
References
Gan, W.-S., & Kuo, S. M. (2006). Teaching DSP software development: From design to fixed-point
implementations. IEEE Transactions on Education, 49(1), 122–131.
https://doi.org/10.1109/TE.2005.863425
ISO/IEC/IEEE. (2011). ISO/IEC/IEEE 60559:2011: Floating-point arithmetic. International Organization for
Standardization.
Texas Instruments. (2024). How to read and interpret digital temperature sensor output data (SBAA588).
Texas Instruments.