presentation
pino capuano
Index
Video
Text + image
Team
Quote
Text + icons
Section break
Audio
Relevant data
Embedded content
Timeline
Interactive question
Graphic + text
Conclusions
Table + text
Closure
List / process
Numerical system (or numeral system): Is a method of rapresanting numbers using a set of symbol or digits in a consistent manner. They provide a way to express quantities and perform arithmetic operations.
Both systems are positional , which means that the value of each digit depends on its position within the number.
Binary
Decimal
decimal system uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
binary system uses only two digits: 0 and 1.
Each digit in this system is called a bit. There position represents a power of 2.
Each digit rapresents powers of 10
345:
- 5 is in the ones place (10^0), so its value is 5 × 10^0 = 5.
- 4 is in the tens place (10^1), so its value is 4 × 10^1 = 40.
- 3 is in the hundreds place (10^2), so its value is 3 × 10^2 = 300.
300+40+5=345.
1101:
- 1 is in the ones place (2^0), so its value is 1×2^0=1.
- 0 is in the twos place (2^1), so its value is 0×2^1=0.
- 1 is in the fours place (2^2), so its value is 1×2^2=4.
- 1 is in the eights place (2^3), so its value is 1×2^3=8.
1101 (in binary)=1+0+4+8=13 (in decimal)
Decimal standard
Binary standard
We have ten fingers, why do our circuits use binary?
Early human attempts at decimal-based computers:
ENIAC：the first general-purpose electronic digital computer, developed in 1945, it could operate using both binary and decimal systems.
IBM 650：one of the first mass-produced computers, introduced in 1954
Why use binary?
0-base and unary
Ternary and higher base
balanced ternary
balanced ternary system：uses three digits: -1, 0, and 1
T is for -1
There’s also a clever approach called balanced ternary. Instead of 0, 1, and 2, it uses -1, 0, and 1. This way, you can jump directly from -1 to 1 without needing a middle state. For example, -1 could mean ‘reverse flow,’ 0 could mean ‘no flow,’ and 1 could mean ‘forward flow.’ Balanced ternary makes transitions smoother, but it’s still more complex than binary and requires extra control. So it’s out as well.
Setun：was a Soviet computer developed in 1958, notable for being the only computer built using a balanced ternary system, which allowed it to perform calculations more efficiently than binary systems in certain cases.
Due to the complexity of hardware implementation, it has not been widely adopted
Analogue and digital
Analog signals are continuous signals, which can take an infinite number of values within a given range.Digital signals are discrete signals, which can take only specific values at distinct intervals.
Is space continuous or discrete?
Theoretically, Planck's constant represents a fundamental limit in quantum mechanics, but it is not directly related to the smallest unit of space. Instead, the Planck length (1.616×10^(−35) meters) is often considered the theoretical minimum scale at which classical concepts of space and time cease to apply. While quantum field theory provides a robust framework for understanding physics at small scales, the discrete or continuous nature of space remains an open question, particularly at Planckian scales where quantum gravity effects become significant.
Whether space is infinitely divisible?
Intuitively, we perceive the world as continuous, smooth like an analog signal. But if we were to increase the resolution, observing at extremely small scales (like zooming in with a super-powerful microscope), who knows—maybe we’d discover ‘pixels.’ Current research hasn’t provided a definite answer. Nevertheless, analog signals as an approximate model are already incredibly useful in daily life and technology, such as in processing sound and images.
Hologram of photon
Analogue technology
Analog technology deals with continuous signals, that is, signals that have no interruptions in time and whose amplitude can take any value within a range.
old televisions
radio broadcasts
Tape recorders
traditional telephone
An analog signal is continuous throughout the transmission process, so even minor interference can directly affect its amplitude. Additionally, analog signals typically lack built-in error detection or correction capabilities.
Turntables
Walkie-Talkies
Digital technology
Digital technology processes discrete signals, that is, signals are divided into a series of finite values, such as binary 0 and 1, which represent information discretely.
PCs
CD
Quantum Computing
Analog signals are more suited for representing natural physical quantities, while digital signals are better suited for storing, processing, and transmitting data within computers.
Bluetooth
Wi-Fi
ADC (Analogue to Digital Converter)
DAC (Digital to Analogue Converter)
- Sampling: The analog signal is measured at regular intervals based on a sampling rate (e.g., 44.1kHz).- Quantization: The sampled values are mapped to a finite set of discrete levels, typically represented by a bit depth (e.g., 16-bit or 24-bit). - Encoding: The quantized values are encoded into binary format for use in digital systems.
- Decoding: The digital signals are converted into discrete analog points.- Smoothing: The discrete points are smoothed into a continuous analog waveform using filters.
Projectors
Supercomputers are designed for maximum computational performance, especially in tasks requiring high-speed floating-point operations. They excel in solving complex scientific problems, such as weather forecasting, molecular simulations, and astrophysical modeling. Supercomputers are built with thousands of processors working in parallel to handle massive datasets and perform intricate calculations at lightning speed. Their primary metric is FLOPS (floating-point operations per second), making them indispensable in cutting-edge research and innovation.
The world's first supercomputer: El capitan
Performance Comparison
El Capitan is approximately 400,000 times more powerful than a high-end personal computer. Tasks that would take years on a personal computer can be completed in hours on El Capitan.
Cost Comparison
El Capitan’s total cost, including hardware, power, and maintenance, runs into hundreds of millions of dollars, designed for governments and advanced research institutions. Personal computers are significantly more affordable, even at the premium range, costing less than one-millionth of El Capitan.
El Capitan’s power requirements match those of a medium-sized city, making it impractical for non-institutional use. Personal computers, on the other hand, are energy-efficient and suitable for everyday environments.
Finish
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Transcript
presentation
pino capuano
Index
Video
Text + image
Team
Quote
Text + icons
Section break
Audio
Relevant data
Embedded content
Timeline
Interactive question
Graphic + text
Conclusions
Table + text
Closure
List / process
Numerical system (or numeral system): Is a method of rapresanting numbers using a set of symbol or digits in a consistent manner. They provide a way to express quantities and perform arithmetic operations.
Both systems are positional , which means that the value of each digit depends on its position within the number.
Binary
Decimal
decimal system uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
binary system uses only two digits: 0 and 1.
Each digit in this system is called a bit. There position represents a power of 2.
Each digit rapresents powers of 10
345:
- 5 is in the ones place (10^0), so its value is 5 × 10^0 = 5.
- 4 is in the tens place (10^1), so its value is 4 × 10^1 = 40.
- 3 is in the hundreds place (10^2), so its value is 3 × 10^2 = 300.
300+40+5=345.1101:
- 1 is in the ones place (2^0), so its value is 1×2^0=1.
- 0 is in the twos place (2^1), so its value is 0×2^1=0.
- 1 is in the fours place (2^2), so its value is 1×2^2=4.
- 1 is in the eights place (2^3), so its value is 1×2^3=8.
1101 (in binary)=1+0+4+8=13 (in decimal)Decimal standard
Binary standard
We have ten fingers, why do our circuits use binary?
Early human attempts at decimal-based computers:
ENIAC：the first general-purpose electronic digital computer, developed in 1945, it could operate using both binary and decimal systems.
IBM 650：one of the first mass-produced computers, introduced in 1954
Why use binary?
0-base and unary
Ternary and higher base
balanced ternary
balanced ternary system：uses three digits: -1, 0, and 1
T is for -1
There’s also a clever approach called balanced ternary. Instead of 0, 1, and 2, it uses -1, 0, and 1. This way, you can jump directly from -1 to 1 without needing a middle state. For example, -1 could mean ‘reverse flow,’ 0 could mean ‘no flow,’ and 1 could mean ‘forward flow.’ Balanced ternary makes transitions smoother, but it’s still more complex than binary and requires extra control. So it’s out as well.
Setun：was a Soviet computer developed in 1958, notable for being the only computer built using a balanced ternary system, which allowed it to perform calculations more efficiently than binary systems in certain cases.
Due to the complexity of hardware implementation, it has not been widely adopted
Analogue and digital
Analog signals are continuous signals, which can take an infinite number of values within a given range.Digital signals are discrete signals, which can take only specific values at distinct intervals.
Is space continuous or discrete?
Theoretically, Planck's constant represents a fundamental limit in quantum mechanics, but it is not directly related to the smallest unit of space. Instead, the Planck length (1.616×10^(−35) meters) is often considered the theoretical minimum scale at which classical concepts of space and time cease to apply. While quantum field theory provides a robust framework for understanding physics at small scales, the discrete or continuous nature of space remains an open question, particularly at Planckian scales where quantum gravity effects become significant.
Whether space is infinitely divisible?
Intuitively, we perceive the world as continuous, smooth like an analog signal. But if we were to increase the resolution, observing at extremely small scales (like zooming in with a super-powerful microscope), who knows—maybe we’d discover ‘pixels.’ Current research hasn’t provided a definite answer. Nevertheless, analog signals as an approximate model are already incredibly useful in daily life and technology, such as in processing sound and images.
Hologram of photon
Analogue technology
Analog technology deals with continuous signals, that is, signals that have no interruptions in time and whose amplitude can take any value within a range.
old televisions
radio broadcasts
Tape recorders
traditional telephone
An analog signal is continuous throughout the transmission process, so even minor interference can directly affect its amplitude. Additionally, analog signals typically lack built-in error detection or correction capabilities.
Turntables
Walkie-Talkies
Digital technology
Digital technology processes discrete signals, that is, signals are divided into a series of finite values, such as binary 0 and 1, which represent information discretely.
PCs
CD
Quantum Computing
Analog signals are more suited for representing natural physical quantities, while digital signals are better suited for storing, processing, and transmitting data within computers.
Bluetooth
Wi-Fi
ADC (Analogue to Digital Converter)
DAC (Digital to Analogue Converter)
- Sampling: The analog signal is measured at regular intervals based on a sampling rate (e.g., 44.1kHz).- Quantization: The sampled values are mapped to a finite set of discrete levels, typically represented by a bit depth (e.g., 16-bit or 24-bit). - Encoding: The quantized values are encoded into binary format for use in digital systems.
- Decoding: The digital signals are converted into discrete analog points.- Smoothing: The discrete points are smoothed into a continuous analog waveform using filters.
Projectors
Supercomputers are designed for maximum computational performance, especially in tasks requiring high-speed floating-point operations. They excel in solving complex scientific problems, such as weather forecasting, molecular simulations, and astrophysical modeling. Supercomputers are built with thousands of processors working in parallel to handle massive datasets and perform intricate calculations at lightning speed. Their primary metric is FLOPS (floating-point operations per second), making them indispensable in cutting-edge research and innovation.
The world's first supercomputer: El capitan
Performance Comparison
El Capitan is approximately 400,000 times more powerful than a high-end personal computer. Tasks that would take years on a personal computer can be completed in hours on El Capitan.
Cost Comparison
El Capitan’s total cost, including hardware, power, and maintenance, runs into hundreds of millions of dollars, designed for governments and advanced research institutions. Personal computers are significantly more affordable, even at the premium range, costing less than one-millionth of El Capitan.
El Capitan’s power requirements match those of a medium-sized city, making it impractical for non-institutional use. Personal computers, on the other hand, are energy-efficient and suitable for everyday environments.
Finish