195 lines
7.1 KiB
Markdown
195 lines
7.1 KiB
Markdown
---
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title: Binary
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TARGET DECK: Obsidian::H&SS
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FILE TAGS: binary
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tags:
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- binary
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---
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## Overview
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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 `1`s in the bit string. Compare the below operation to the method for converting from one numerical base to another (e.g. [[radices#Hexadecimal|hexadecimal]]).
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```c
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unsigned int bit_weight(int64_t n) {
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unsigned int count = 0;
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while (n) {
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count += (n % 2 == 0) ? 0 : 1;
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n /= 2;
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}
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return count;
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}
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```
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%%ANKI
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Basic
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Why is a "bit" named the way it is?
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Back: It is short for **b**inary dig**it**.
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Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
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<!--ID: 1707432641557-->
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END%%
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%%ANKI
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Basic
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What does the weight of a bit string refer to?
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Back: The number of `1`s in the string.
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Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
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<!--ID: 1708366788645-->
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END%%
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%%ANKI
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Basic
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How might you use C to find the weight of a bit string?
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Back: Repeatedly divide by `2`, counting all remainders of `1`.
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Reference: Oscar Levin, *Discrete Mathematics: An Open Introduction*, 3rd ed., n.d., [https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf).
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Tags: c17
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<!--ID: 1708366788648-->
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END%%
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%%ANKI
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Cloze
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A byte consists of {8} bits.
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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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<!--ID: 1707432641557-->
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END%%
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%%ANKI
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Cloze
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A byte consists of {2} nibbles.
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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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<!--ID: 1707432641560-->
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END%%
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%%ANKI
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Cloze
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A nibble consists of {4} bits.
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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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<!--ID: 1707432641562-->
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END%%
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%%ANKI
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Basic
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What process is used to convert from e.g. decimal to another base?
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Back: Divide repeatedly by the base. Maintain remainders right to left.
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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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<!--ID: 1707432641591-->
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END%%
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%%ANKI
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Basic
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Why does converting from e.g. decimal to another base involve repeated division?
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Back: The position of a digit corresponds to the base raised to that position.
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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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<!--ID: 1707432641592-->
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END%%
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## Endianness
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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.
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%%ANKI
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Basic
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Platforms with multi-byte objects must establish what two conventions?
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Back: The object's address and byte ordering.
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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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<!--ID: 1707661283766-->
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END%%
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%%ANKI
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Basic
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How are multi-byte objects typically addressed?
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Back: By the smallest address of the bytes used.
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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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<!--ID: 1707661283768-->
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END%%
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%%ANKI
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Basic
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How are bytes of multi-byte objects typically ordered?
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Back: As big-endian or little-endian.
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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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<!--ID: 1707661283770-->
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END%%
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%%ANKI
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Basic
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What is endianness?
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Back: The ordering of bytes of a multi-byte object.
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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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<!--ID: 1707661283771-->
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END%%
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%%ANKI
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Basic
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What does it mean for a byte to be "most significant"?
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Back: It contribute most to the byte's (decimal) value.
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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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<!--ID: 1707661283773-->
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END%%
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%%ANKI
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Basic
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What does it mean for a byte to be "least significant"?
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Back: It contribute least to the byte's (decimal) value.
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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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<!--ID: 1707661283774-->
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END%%
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%%ANKI
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Basic
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What does it mean to be big-endian?
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Back: The most significant byte is ordered first.
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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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<!--ID: 1707661283776-->
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END%%
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%%ANKI
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Basic
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What does it mean to be little-endian?
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Back: The least significant byte is ordered first.
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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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<!--ID: 1707661283777-->
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END%%
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%%ANKI
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Basic
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How are bytes of `int32_t x = 0x01234567` written in big-endian?
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Back: `0x01 0x23 0x45 0x67`
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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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Tags: c17
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<!--ID: 1707661283779-->
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END%%
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%%ANKI
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Basic
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How are bytes of `int32_t x = 0x01234567` written in little-endian?
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Back: `0x67 0x45 0x23 0x01`
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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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Tags: c17
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<!--ID: 1707661283780-->
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END%%
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%%ANKI
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Cloze
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Many microprocessors chips are {bi-endian} meaning they can be {configured as either big- or little-endian}.
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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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<!--ID: 1707661283782-->
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END%%
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```c
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#include <stdint.h>
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#include <stdio.h>
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int main() {
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int32_t x = 0x01234567;
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for (int i = 0; i < 4; ++i) {
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printf("%.2x ", ((unsigned char *)(&x))[i]);
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}
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}
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```
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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`.
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## Bibliography
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* Bryant, Randal E., and David O'Hallaron. *Computer Systems: A Programmer's Perspective*. Third edition, Global edition. Always Learning. Pearson, 2016. |