1. Number Systems Binary to Decimal Octal to Decimal Hexadecimal to Decimal Binary to Octal Binary to Hexadecimal Two’s Complement

2. Binary to Decimal Rule 25 ‑ 1: In converting from binary to decimal, find the value or weight of the MSB. Work down to the LSB, adding the weight of that position if a 1 is present or a 0 if a 0 is present. 101 2 = 1 x 2 2 +0 x 2 1 +1 x 2 0 = 5 10

3. Octal to Decimal Rule 25 ‑ 2: In converting from octal to decimal, find the weight of the digit in each position. Add the values of the digits in each position to determine the decimal equivalent. 473 8 = 4 x 8 2 7 x 8 1 3 x 8 0 = 315 10

4. Hexadecimal to Decimal Rule 25 ‑ 3: In converting from hexadecimal to decimal, find the weight of the digit in each position. Add the values of the digits in each position to determine the decimal equivalent. 2BC 16 = 2 x 16 2 +11 x 16 1 +12 x 16 0 = 700 10

5. Binary to Octal Key Point: To convert from binary to octal, separate the bits into 3 ‑ bit groups, starting with the LSB and moving left to the MSB. 10110110 2 = 10 | 110 | 110 2 = = 266 8

6. Binary to Hexadecimal Key Point: To convert from binary to hexadecimal, separate the bits into 4 ‑ bit groups, starting with the LSB and moving left to the MSB. 10011011 2 = 1001 | 1011 2 = = 9B 16

7. Key Point: Computers subtract by using the two's complement method. The two's complement of the subtrahend is added to the minuend. The carry out of the MSB is ignored. 01100111 – 01001010 Solution: 01100111 (+)10110110 (Two’s complement) 1 00011101 (Difference) Two’s Complement