A. Introduction

1 octal digit can be turned into 3 binary digits because 2^3=8.

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

1 hexadecimal digit can be mapped with 4 binary digits because 2^4=16

0000[0], 0001[1], 0010[2], 0011[3], 0100[4], 0101[5], 0110[6], 0111[7]

1000[8], 1001[9], 1010[A], 1011[B], 1100[C], 1101[D], 1110[E], 1111[F]

B. Conversion

From Octal / Hex to Binary: replace each digit the corresponding binary digits as above

From Binary to Octal / Hex: starting from the rightmost digit, turn every 3 or 4 digits into the corresponding Octal / Hex digit. Supply leading 0's as necessary.

From Octal to Hex: use Binary as a bridge.

C. Try:

1. A6

2. 4DE

3. a) 100010 b) 11010 c) 1011100 d) 1011 e) 10001100; bcd

4. 168C18

5. 10001001111

6. 5

1.0A6

2.4BD

3.

4.168C14

5.11010001111

6.1018

Good work everyone, I know the calculation could be challenge when you switch among different systems. Below are the correct answers for reference.

1. 0A6 or A6

2. 4CE

3. a) 100010 b) 111010 c) 1011100 d) 1011 e) 10001100; bcd

4. 168C14

5. 10001001111

6. A

1)A6

2)4CE

3)a)100010 b)111010 c)1011100 d)1011 e)10001100----b,c,d

4)168C14

5)10001001111

6)A

1. A6

2. 532 (16) - 64 (16) = 4CE

3. A. 100010 B. 111010 C. 1011100 D. 1011 E. 10001100

Numbers with more 1 than 0: 111010, 1011100, 1011

4. 168C14

5. 10001001111

6. A