Question

1. Using only half adders, design a four-bit incrementer circuit (a circuit that adds 1 to a four- bit binary number). 2. Using only 2-to-4 line decoders with enable, construct a 4-to-16 line decoder. 3. Using a decoder and external gates, design the combinational circuit defined by the following three Boolean functions: F = x'y'z' + x2 F2 = xy'z' + x'y F3 = x'y'z + xy

Answer 1

(Q) (1) 4-bit Incrementer circuit (using only half adders): - 4 bit binary number = Az A A A Addition of Az A₂ A, do with 1. SHAY HAB HAZ Idolla ailao HAI Coul S3 S2 Si so circuit is created by cascading 4 So 4bit ancrementer half adder circuits Implementatim diaqramo AO Cout

(2) 440 16 lúne decoder using 2x4 line decoder a(0) - ac] MC] 41] Y 4(3) 2xy En z w[6) aloj - w(1) 4[5] Y[6] YE аху w(31. - 4(8) -Y[9] aca 2x4 Y(10) 4 [12] - Y(13] aco 244 Y(14) 4(15) En

. (3) amplementation of boolean function using decoder and External gateso i fi = n'y'z'taz This is a variable boolean function. so we use 3x8 decoder and External gates. Truth Table n y z ħ Ý Ž 1.4. Į nz fi ta of wes - ooooooo- 1 0 1 0 1 0 1 1 1 1 0 0 0 1 1 fi= [ (0,5,7) fi= q (mo, m5, ma)

Amplementations 3x8 my decoder ma di) fg - nyla'taly :- Truth tables n y z ¢ ¥ 2y z' x'y F2 2010 101 3 0 1 1 1 0 0 4 1 0 0 0 1 1 5 0 1 0 1 0 6 1 1 0 0 0 1 7 1 1 1 0 0 0 oo-ool oo - - 0 0 0 0 0 fa= {(m2, m3, m4)

implementation's mo m) ma 3 xe my decoder mb ma (і) с, туа - 12'- Truth table учаячуу1 195 - - o 3 от то ч Тооо 5 тот от стi o o o o - oo o o oo - - o ooo - от - 1 +2 = 2 ( mi, me , ma)

statim: 0 m ) EW 8x & hu mb ma