Question

Convert the following three hexadecimal numbers to both binary and decimal. (Hint: it is probably easier to convert hex to binary first, then convert binary to decimal.) Show your work:

3e 3e0 3e00.
In bullet points, tell what you observe about the relationships among the decimal values of these numbers.

Answer 1

3e : 00111110 (62)

3e0 : 0000001111100000 (992)

3e00 : 0011111000000000 (15872)

Step-by-step explanation:

Converting the given hexadecimal numbers to binary and decimal format:

1) 3e

3-> 0011

e-> 1110

Combining , 3e -> 00111110

This can be converted to decimal by multiplying each 1 in the binary representation by 2^(position -1) and adding the results.

So 3e = 32+16+8+4+2 = 62

2) 3e0

Binary => 0000001111100000

Converting to decimal : 992 [ This is 16 times a]

3) 3e00

Binary => 0011111000000000

Converting to decimal : 15872 [ This is 16 times b]

So adding a 0 to the hex representation multiplies the decimal number by 16.