There are five parts to this Submit them with the rest of the assignment on canv

Question

There are five parts to this Submit them with the rest of the assignment on canvas. assignment and each is required. You must show your work to get credit. From Chapter 1 of the text: I. For the integer representation section, do this problem: You are given an eight-bit binary (2's complement) value of 11111110 What is its value in the following representations .hexadecimal signed decimal unsigned decimal base 5 (assume the binary value is interpreted as unsigned) If the value is assumed to be signed and is converted to 32 bits, what is its hexadecimal value after conversion? The basic laws of Boolean algebra are listed below. Note that inverse can be expressed any of three ways: with a bar on top, with a appended, or with a prefix. Thus, B, B', ~B are equivalent. Similarly, the inverse of the product AB can be expressed (AB) Identity law: A + 0 A and A1 = A * Zero and one law: A + 1 1 and A0 = 0 Inverse laws: A + A' = 1 and AA' = 0 Commutative law: A + B = B + A and AB = BA Associative law: A + (B + C) = (A + B) + C and A(BC)-(AB)C . Distributive law: A(B + C) = AB + AC and A + BC = (A + B)(A + C) . DeMorgan's Theorem: (A+ B)' = A'B' and (AB)' = A. B' Below are three logic equations. For each, design and draw a combinational circuit for the beginning equation using standard gates reduce the equation as much as possible using Boolean Algebra. You will find the identities and associative, commutative and distributive laws particularly useful. using a truth table, verify that your reduced equation is equivalent to the original .design and draw a combinational circuit for the reduced equation using standard AND, OR and NOT gates . redesign it only for problem 1. below. the combinational circuit for the reduced equation using the universal gate NAND, do 2. (C + B')(B+ C') (multiply out first) 3. AC' + BD'+AB+BD + AC+ BC+ CD (rearrange and factor) 4. AB +CAB+ have A before B before C, then combine) BA' +A'CB (rearrange (commutative) so that all terms

Explanation / Answer

Solution:

The first question is done as per Chegg guidelines, please repost others.

Part 1:

The number which we have is

11111110

a)

Hexadecimal:

To convert binary from hexadecimal, we just need to categorize the binary number into 4 bits of set from LSB and if there are not a 4 bits left at the MSB chunk then we can append 0's.

After that each 4 bit number is converted ti its equivalent hexadecimal number

son

1111 1110 = FE in hex.

b)

signed decimal:

If we talk about signed decimal the MSB of the binary number is considered to be the sign so if it is 1 means negative number, positive otherwise.

1 1111110 = 0*2^0 + 1*2^1 + 1*2^2 + 1*2^3 + 1*2^4 + 1*2^5 + 1*2^6 = -126

unsigned decimal:
Unsigned decimal is directly converted

so

11111110 = 0*2^0 + 1*2^1 + 1*2^2 + 1*2^3 + 1*2^4 + 1*2^5 + 1*2^6 + 2*2^7 = 254

base 5:

2004

if the value is signed and changed to 32 bit then hexadecimal value of the conversion will be

1111 1111 1111 1111 1111 1111 1111 1110=> FFFFFFFE

Explanation:

If the number is signed to change 8-bit number to 32 bits we have to append the rest of the MSBs with the MSB which is 1.

I hope this helps if you find any problem. Please comment below. Don't forget to give a thumbs up if you liked it. :)

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