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.

1012 = 1 x 22

+0 x 21

+1 x 20 = 510

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.

4738 = 4 x 82

7 x 81

3 x 80 = 31510

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.

2BC16 = 2 x 162

+11 x 161

+12 x 160 = 70010

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.

101101102 =

10 | 110 | 1102 =

= 2668

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.

100110112 =

1001|10112=

= 9B16

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