Digital Logic · topic
Positional systems and base conversion (integer and fraction parts, grouping for octal and hex, unknown-base equations), unsigned, sign-magnitude, 1's and 2's complement ranges and readings, r's and (r-1)'s complements, sign extension, excess-K, and the codes BCD, excess-3, 2421 and Gray with BCD addition.
Positional value of a base-r numeral, the valid digit set, integer conversion by repeated division and fraction conversion by repeated multiplication, when a fraction terminates in a base, grouping between binary, octal and hex (including fractional parts), unknown-base equations and counting their solutions, digits needed for a number, and quick powers of two. Every value checked by script.
A partial preview of the top of the sheet. The full sheet is in the Digital Logic cheat sheet pack.
Unsigned, sign-magnitude, 1's complement, 2's complement and excess-K (biased) integers: ranges for n bits, number of zeros, reading one pattern in every form, negation rules and the 2's complement weight formula, sign extension, r's and (r-1)'s complements in any base, subtraction by complement addition with and without end carry, and byte order (endianness). Every value checked by script.
A partial preview of the top of the sheet. The full sheet is in the Digital Logic cheat sheet pack.
Weighted and unweighted decimal codes: 8421 BCD with its invalid patterns and bit cost, BCD addition with the +6 correction and its detection function, excess-3 and 2421 as self-complementing codes, excess-3 addition, Gray code construction and both conversions, the unit-distance property and its link to K-map order, parity bits and Hamming distance rules. Every code table and sum checked by script.
A partial preview of the top of the sheet. The full sheet is in the Digital Logic cheat sheet pack.
