Question

You have been asked to design a simpler version of the 7-segment display that can be used to display the “tens digit” of the minutes of a digital clock (so, display the digits 0 through 5). 1. Use kmaps to find the simplest SOP form of the functions for the circuit for the segments C and g. 2. Draw the circuits you designed. 3. What is the number of gates and literals needed to implement the two functions? 4. If the functions were implemented using an appropriate-sized decoder, how many gates and literals would be needed? (Internal and External) 5. If the functions were implemented using appropriate sized MUXs, how many gates and literals would be needed? (Internal and External)

Answer 1

Tsegment display fl el 9 Ic с d X Y Z ABC с os O O fl-16 el 1 cl d 1 b=1 ol I cal a=1 gall b=1 o ell d=1 0 1 - 911 11 - I O o I- galcal o ) 1 gol lal

1) for sop of c 42 oo It lo O c=y+2 for sop of g 42 oo oL L 10 X 0 g=xty yo)) Z 7 g 3) for a Number of gates = = 2 Number of literals=2 for Number of gates = 1 Number of literals=2

4 ) c=742 g=xty = 7+2 =X+Y Y. = x4 2-4 Decoder Ao Do zt AN 7 'YZ y D2 I 03. Number of internal gates ga = 6 External gotes = 1 Number of internal literals: 2 CAO, A1 External literals = 2 (412) X Do x D 1 g A)

Number of internal gates = 6 External gotes = 1 Nember of internal literals= 2 CAO, A1) External literals=2 xiy g= c=y. 2:1 MUX So - Z Io Đ yoz 1% o I Number of internal gotes = 4 External gates=1 Internal literals = 3 Co, IO,II) External literals = 3 (214,0) 2:1 MOX у so Io XoY co 1 Number of internal gates = 4 External gotes=2 internal literals :3 (So, Io, IV External literals=3 (Y,X, 0)