Give an example 8bit nonpositional binary representation of

Give an example 8-bit non-positional binary representation of a number 8_10. (b) Find the binary and hexadecimal representations for a decimal number, 61254_10. (c) In Planet Y, people use a base-Y positional number system for positive integers (Y is a positive integer). If 130_Y = 40_DEC, determine the value of Y.

Solution

(a) 8₁₀  = (00001000)₂

(b) 61254 = (1110111101000110)₂    = (EF46)₁₆

(c) Given 130_y = 40₁₀

you can write 130_y as a 0*y⁰ + 3* y¹ + 1*y² = 40

Y² + 3*Y -40 =0

By solving these we will get y = -8,5

Y can\'t be negative. Hence, Y =5 is valid