Question

Which of the following value is not equal to (7214)₈?
1. (111010001100)₂
2. (EAC)₁₆
3. (3724)₁₀
4. (322030)₄

Answer 1

Correct Answer - Option 2 : (EAC)₁₆

(7214)₈ = 7 × 8³ + 2 × 82 + 1 × 81 + 4 × 80 = (3724)₁₀

Option 2: 

(EAC)16 = E × 162 + A × 161 + C × 160

(EAC)16 = 14 × 162 + 10 × 161 + 12 × 160 = (3756)10

Therefore (EAC)16 is not equal to (7214)8?

Binary to Octal conversion table:

000	001	010	011	100	101	110	111
0	1	2	3	4	5	6	7

 

Binary to Hexadecimal conversion table:

0000	0001	0010	0011	0100	0101	0110	0111	1000	1001	1010	1011	1100	1101	1110	1111
0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F

Tips and Tricks:

Every digit in octal represents 3 bits of binary and every digit in hexadecimal is 4 bits in binary

(513)8 = (101 001 011)2

Forming pairs of 4 to get the hexadecimal representation, we get:

(111  010  001  100)2  =  (1110  1000  1100)2 = (14B)16 = (E 8 C)16