Prom Chapter 1 of the text 1. For the integer representation section, do this pr
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Question
Prom Chapter 1 of the text 1. For the integer representation section, do this problem: You are given an eight-bit binary complement) value of 11111110 What is its value in the following representations. .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? Part Two (15 points) boolean algebra 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 Al-A . Zero and one law: A+1 1 and AO . Inverse laws: A + A' = 1 and AA 0 Commutative law: A + B-B + A and ABBA law: A + (B + C) = (A + B) + C and A(BC) = (ABC Distributive law: A(B +C) AB +AC and A + BC (A+B)(A+C) . DeMorgan's Theorem: (A + B), = AB, 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, verity 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 the combinational circuit for the reduced equation using the universal gate NAND, do it only for problem 1. belowExplanation / 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.
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