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

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 = 1 x x x 2 0 = 5 10

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 = 4 x x x 8 0 =

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 x x 16 0 =

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 = 10 | 110 | = = 266 8

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 = 1001 | = = 9B 16

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 – Solution: (+) (Two’s complement) (Difference) Two’s Complement