Question

Please, multiply the highlighted yellow digit by 6 first then solve. thank you!

Given: A4-bit adder is implemented in a carry ripple style as shown in the figure below. B3 A3 B2 A2 B1 A1 BO AO FA c3 FA FA FA CO='1' s2 s1 SO Sought: Please calculate the output carries for each full adder (FA) using A=0x01 and B=0x04. It is required to show ALL incremental steps of the solution, then record each the final results in the table below. C4 C3 C2 ci

Answer 1

Full adder circuit is as follows:

А. Sum INPUT full-Adder Circuit OUTPUT Carry Out B Carry In

The truth table of full adder is as follows:

Full Adder Truth table INPUTS OUTPUTS А. B Cin SUM CARRY OUT 0 0 0 0 0 0 0 1 1 0 O 1 0 1 0 1 1 0 1 1 0 1 0 O 1 0 1 0 1 1 0 0 1 1 1 1 1 1

From the truth table, we can write: Ly Sum(s) = Ā B Cin + Ā Bcin + ABCin + ABC in S = Ā[@Cin+Ban ] + a[Bein + BCin] Let Z = BCin+ Brin B Tin => z=B0 Cin then 6 denotes XOR Z = B cin + Bein Now we can write x0y = xj tły S = ĀZ+ AŽ S = AAZ S = A B Cin 4 Carry-out (Cout) = AB + Acin+ BCin Cout AB+ Cin (A+B)

A= 0x01 and B = 0x04 -You have mentioned that this question is to be solved after multiplying A=0x01 by 6. Here a represent 0x01 = (1) 10 So after multiplying it by 6 we get (6) 10 which is A =0006 in hexadecimal. - In binary system; А 0110 in order A,A,A, A. B - 0100 in order B₂B, B, Bo Co= '1'. Given that initial carry From above expression) Bo to Here bits & we FALK co expression we can directly add the Il can use the СІ Ao=0 Bo=0 Co=1. So by direct adding by expression ootte C = A Boo (Aot Bo) = 0.0 + 1.(0+0) Carry + 1.0 So 0 + D Sum So = 1 c=0 = =0 Remember that in using expression) + denotes 'OR' operation denotes 'AND' operation he got le=0

B, A, A = 1 B=0 G=0 FA₂K CI = A,B, + C, (A, +B) = 1.0+ 0.(1+0) Si + o We got ₂ B₂ A2 A=1 B₂ = 1 C=0 C3 FARK C₂ C₂ = A₂B₂ + C₂ (A₂+B₂) = 1.1 +0. (1+1) = 1 +o S₂ he got (C3= 1 jv Az=0 B=0 B3 A3 Il FA4 K -CZ C3=1 Cy= A,B3 + Cz. (Az+B3) = 0.0 + 1. (oto) 0+ 0 S kle got Cy=0 Therefore answer is Calea G 0 o

According to the question we need not determine the value of SUM in each case, so I haven't obtained the values of S₃, S₂, S₁ and S₀. In case you need them, you can use the expression obtained for SUM.