--- title: Binary TARGET DECK: Obsidian::STEM FILE TAGS: binary tags: - 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 `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]]). ```c 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 **b**inary dig**it**. 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). END%% %%ANKI Basic What does the weight of a bit string refer to? Back: The number of `1`s in the string. 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). 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](https://discrete.openmathbooks.org/pdfs/dmoi3-tablet.pdf). Tags: c17 END%% %%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. END%% %%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. END%% %%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. END%% %%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 END%% %%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](https://en.wikipedia.org/w/index.php?title=Endianness&oldid=1264018894). 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](https://en.wikipedia.org/w/index.php?title=Endianness&oldid=1264018894). 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](https://en.wikipedia.org/w/index.php?title=Endianness&oldid=1264018894). 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](https://en.wikipedia.org/w/index.php?title=Endianness&oldid=1264018894). 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](https://en.wikipedia.org/w/index.php?title=Endianness&oldid=1264018894). END%% ```c #include #include 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](https://en.wikipedia.org/w/index.php?title=Endianness&oldid=1264018894).