8.9 KiB
| title | TARGET DECK | FILE TAGS | tags | |
|---|---|---|---|---|
| Binary | Obsidian::STEM | binary |
|
Overview
A binary digit or bit is a 0 or 1 character. A bit string is then a contiguous sequence of bits. It's weight is a reference to the number of 1s in the bit string. Compare the below operation to the method for converting from one numerical base to another (e.g. radices#Hexadecimal).
unsigned int bit_weight(int64_t n) {
unsigned int count = 0;
while (n) {
count += (n % 2 == 0) ? 0 : 1;
n /= 2;
}
return count;
}
%%ANKI Basic Why is a "bit" named the way it is? Back: It is short for binary digit. Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
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%%ANKI
Basic
What does the weight of a bit string refer to?
Back: The number of 1s in the string.
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
END%%
%%ANKI
Basic
How might you use C to find the weight of a bit string?
Back: Repeatedly divide by 2, counting all remainders of 1.
Reference: Oscar Levin, Discrete Mathematics: An Open Introduction, 3rd ed., n.d., https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf.
Tags: c17
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%%ANKI Cloze A byte consists of {8} bits. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
%%ANKI Cloze A byte consists of {2} nibbles. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
%%ANKI Cloze A nibble consists of {4} bits. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
%%ANKI Basic What process is used to convert from e.g. decimal to another base? Back: Divide repeatedly by the base. Maintain remainders right to left. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
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%%ANKI Basic Why does converting from e.g. decimal to another base involve repeated division? Back: The position of a digit corresponds to the base raised to that position. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
Endianness
Platforms with multi-byte objects must establish the object's address and byte ordering. Objects are typically addressed by the smallest address of the bytes used. Bytes are ordered either in big-endian or little-endian. In big-endian, the most significant byte is listed first. In little-endian, the least significant byte is ordered first.
%%ANKI Basic Platforms with multi-byte objects must establish what two conventions? Back: The object's address and byte ordering. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
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%%ANKI Basic How are multi-byte objects typically addressed? Back: By the smallest address of the bytes used. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
%%ANKI Basic How are bytes of multi-byte objects typically ordered? Back: As big-endian or little-endian. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
%%ANKI Basic What is endianness? Back: The ordering of bytes of a multi-byte object. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
%%ANKI Basic What does it mean for a byte to be "most significant"? Back: It contribute most to the byte's (decimal) value. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
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%%ANKI Basic What does it mean for a byte to be "least significant"? Back: It contribute least to the byte's (decimal) value. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
%%ANKI Basic What does it mean to be big-endian? Back: The most significant byte is ordered first. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
%%ANKI Basic What does it mean to be little-endian? Back: The least significant byte is ordered first. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
%%ANKI
Basic
How are bytes of int32_t x = 0x01234567 written in big-endian?
Back: 0x01 0x23 0x45 0x67
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
END%%
%%ANKI
Basic
How are bytes of int32_t x = 0x01234567 written in little-endian?
Back: 0x67 0x45 0x23 0x01
Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
Tags: c17
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%%ANKI Cloze Many microprocessors chips are {bi-endian} meaning they can be {configured as either big- or little-endian}. Reference: Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
END%%
%%ANKI Cloze A big-endian system stores the {most} significant byte at the {smallest} memory address. Reference: “Endianness,” in Wikipedia, December 19, 2024, https://en.wikipedia.org/w/index.php?title=Endianness.
END%%
%%ANKI Cloze A big-endian system stores the {least} significant byte at the {largest} memory address. Reference: “Endianness,” in Wikipedia, December 19, 2024, https://en.wikipedia.org/w/index.php?title=Endianness.
END%%
%%ANKI Cloze A little-endian system stores the {least} significant byte at the {smallest} memory address. Reference: “Endianness,” in Wikipedia, December 19, 2024, https://en.wikipedia.org/w/index.php?title=Endianness.
END%%
%%ANKI Cloze A little-endian system stores the {most} significant byte at the {largest} memory address. Reference: “Endianness,” in Wikipedia, December 19, 2024, https://en.wikipedia.org/w/index.php?title=Endianness.
END%%
%%ANKI Basic Which of little- or big-endian more closely mirrors the way numbers are written in English? Back: Big-endian. Reference: “Endianness,” in Wikipedia, December 19, 2024, https://en.wikipedia.org/w/index.php?title=Endianness.
END%%
#include <stdint.h>
#include <stdio.h>
int main() {
int32_t x = 0x01234567;
for (int i = 0; i < 4; ++i) {
printf("%.2x ", ((unsigned char *)(&x))[i]);
}
}
The above snippet can be used to check endianness on the current machine. If big-endian, the output should be 01 23 45 67. If little-endian, 67 45 23 01.
Bibliography
- Bryant, Randal E., and David O'Hallaron. Computer Systems: A Programmer's Perspective. Third edition, Global edition. Always Learning. Pearson, 2016.
- “Endianness,” in Wikipedia, December 19, 2024, https://en.wikipedia.org/w/index.php?title=Endianness.