Implement the following truth table in figure HW$8\mathrm{.}1$ with a $4$:$1$ MUX.

A B C F

$0001$

$0010$

$0100$

$0111$

$1001$

$1011$

$1100$

$1110$

Figure HW$8\mathrm{.}1$

$2..$ Realize $4$ switching functions using the ROM: Populate ROM Cells, Label Outs & Ins

F$1=$m$(0,1,3,5,13,15)$ F$2=$m$(1,3,4,6,9,11)$ F$3=$m$(3,5,9,13,14,15)$ F$4=$m$(5,7,13,15)$

Also fill in the Truth Table, only put the $1$s leave $0$s blank.

Figure HW$8\mathrm{.}2$ Truth table with $4$ output functions

A B C D F$1$ F$2$ F$3$ F$4$

$0000$

$0001$

$0010$

$0011$

$0100$

$0101$

$0110$

$0111$

$1000$

$1001$

$1010$

$1011$

$1100$

$1101$

$1110$

$1111$

O$0$ O$1$ O$2$ O$3$

O$1$

O$1$

Address

Lines

ROM

Contents

Answer the following questions about the ROM:

a$)$ How many rows in the ROM

b$)$ How many columns in the ROM

c$)$ How many address lines to the ROM

d$)$ How many Outputs from the ROM

e$)$ How many bits does the ROM hold

Label the inputs and the $2$ control lines

with the correct variables or constants