Chapter 3

Question 1

literal

Answer 1

each appearance of a variable in a term
xy’z has three literals

Question 2

K-map

Answer 2

Karnaugh map
used to minimize gates for a function

Question 3

why are the minterms placed where they are in a kmap

Answer 3

to make sure there is only one bit changing between each adjacent square

Question 4

kmaps with minterms

Answer 4

• take SOP/all the minterms when the output is 1 and mark as 1 on kmap
• group 1’s into largest groups that are the size of 2^n then find expression for each grouping and add them
• circled groupings can wrap off top, bottom, sides and corners of the grip onto opposing sides

Question 5

dont care conditions

Answer 5

• for some functions, the output is not specified for some input combinations
• mark as an x on k-map and they can be taken as either a 0 or 1, whichever best simplifies the function

Question 6

odd function

Answer 6

• multivariable XOR (ex-OR) function
• 1 if an odd number of inputs is 1

Question 7

even function

Answer 7

• complement of the entire XOR function
• aka put brackets around entire odd function then complement it

Question 8

what are ex-or functions useful for

Answer 8

• detecting errors using parity bits
• the even parity bit of a string variables is all variables xored with eachother
• parity bit can be checked by xoring all variables and the parity bit

Question 9

k-maps for POS

Answer 9

• place 1’s for each minterm
• fill in all other spaces with zeroes
• simplify kmap using the zeroes instead of 1s
• will get a sum of products from the kmap, so must complement simplified function to get POS