Problem 3 [Conversions] (10 points) (a) Give an example 16-bit non-positional bi

Question

Problem 3 [Conversions] (10 points) (a) Give an example 16-bit non-positional binary representation of a number 1210

(b) Find the binary and hexadecimal representations for a decimal number, 6124510.

(c) In Planet Y, people use a base-Y positional number system for positive integers (Y is a positive integer). If 316base Y = 160base10, determine the value of Y.

Problem 3 [Conversions] (10 points) (a) Give an example 16-bit non-positional binary representation of a number 1210. [2 points] (b) Find the binary and hexadecimal representations for a decimal number, 6124510. [4 points] (c) In Planet Y, people use a base-Y positional number system for positive integers (Y is a positive integer). If 316base Y 160base 0, determine the value ofY. [6 points]

Explanation / Answer

(a)

1210

convert to binary with base 2

------------------ remainder

2|12

2|6 ----- 0

2|3 -----0

2|1    ------1

2|0    ------1

= (1100)2

16 bit binary number = (0000 0000 0000 1100)2

b)

--------------------remainder

2|61245

2|30622    ---- 1

2|15311    ------0

2|7655    ------1

2|3827    -------1

2|1913 -------1

2|956    --------1

2|478    ------0

2|239    ------ 0

2|119    ----- 1

2|59 ------1

2|29 ------1

2|14 ------1

2|7    ------ 0

2|3 ------ 1

2|1 ------ 1

2|0    ----1

binary = (1110 1111 0011 1101)2

Hexadecimal = (EF3D)16

c)

316y = 16010

3*y2 + 1*y + 6 = 160

3y2 + y -154 = 0

y = 7, -22/3

discard -22/3 as it cannot be base

so base y = 7

3167 = 3*49 + 7 + 6 = 147 + 13 = 16010

Do ask if any doubt. Please upvote.

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