1. Binary01.ppt Decimal Decimal: Base 10 means 10 Unique numerical digits 0 1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 101001,00010,000 Weight Positions 3, 4 6 7 10 3 x 1000 = 3000 4 x 100 = 400 6 x 10 = 60 7 x 1 = 7 ------------------------ 3,467 etc.

2. Binary01.ppt Decimal Addition 0 1 2 3 4 5 6 7 8 9 3 + 5 --------- 8 start +1+2+3+4+5 6 + 7 --------- 13 0 1 2 3 4 5 6 7 8 9 start+1+2+3+6+7+4+5 Carry 1

3. Binary01.ppt Binary Decimal: Base 2 means 2 Unique numerical digits 0 1 On Off In Out Left Right 1 1 1 1 2 4 816 Decimal Weight Positions 32 etc. 1 0 1 1 0 1 2 1 x 32 = 32 0 x 16 = 0 1 x 8 = 8 1 x 4 = 4 0 x 2 = 0 1 x 1 = 1 ------------------------ 45 10

4. Binary01.ppt Binary Addition 0 + 0 ------ 0 1 + 0 ------ 1 0 + 1 ------ 1 1 1 + 1 ------ 1 0 with a 1 carry 1 0 1 1 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 Carry

5. Binary01.ppt Hexadecimal Decimal: Base 16 means 16 Unique numerical digits 0 1 2 3 4 5 6 7 8 9 A B C D E F Decimal Equivalents 0 = 0 1 = 1 2 = 2 3 = 3 4 = 4 5 = 5 6 = 6 7 = 7 8 = 8 9 = 9 A = 10 B = 11 C = 12 D = 13 E = 14 F = 15

6. Binary01.ppt Hexadecimal 0-F 0-F 0-F 0-F 0-F 0-F 1,048,576 65,536 4,096 256 16 1 Decimal Weight Positions A 3 9 D 6 C 16 A = 10 X 1,048,576 = 10,485,760 + 3 = 3 X 65,536 = 196,608 + 9 = 9 X 4096 = 36,864 + D = 13 X 256 = 3,328 + 6 = 6 X 16 = 96 + C = 12 X 1 = 12 ------------------------------------------------------ 10,722,668 10

7. Binary01.ppt Hexadecimal to Binary 0 = 0000 1 = 0001 2 = 0010 3 = 0011 4 = 0100 5 = 0101 6 = 0110 7 = 0111 8 = 1000 9 = 1001 A = 1010 B = 1011 C = 1100 D = 1101 E = 1110 F = 1111 It takes 4 bits to make one Hex number

8. Binary01.ppt Octal Decimal: Base 8 means 8 Unique numerical digits 0 1 2 3 4 5 6 7 Decimal Equivalents 0 = 0 1 = 1 2 = 2 3 = 3 4 = 4 5 = 5 6 = 6 7 = 7 Octal to Binary 0 = 000 1 = 001 2 = 010 3 = 011 4 = 100 5 = 101 6 = 110 7 = 111 It takes 3 bits to make one Octal number

9. Binary01.ppt 1 1 1 1 1 864512 Decimal Weight Positions Octal 7 5 2 3 8 7 x 512 = 3,584 16 x 5 = 80 2 x 8 = 16 3 x 1 = 3 ------- 3,683 10

10. Binary01.ppt Binary to Decimal 1 0 1 1 0 1 0 1 Decimal Weights 128 32 16 4 1 = 181 10 Add the decimal weights of the “1” bits Decimal to Binary 1. Find the largest binary bit that will fit in the number without going over the number 2. Mark that bit as “on” and subtract the bit weight value from the decimal number 3. Repeat steps 1 and 2 until there are no more numbers remaining in the decimal number

11. Binary01.ppt Hex to Binary C 5 9 B 16 1100 0101 1001 1011 2 = Convert Hex to Binary Binary to Hex Divide bits into groups of 4 1100010110011011 2 C 5 9 B 16 1. 2. 3. 1100 0101 1001 1011 2

12. Binary01.ppt Binary to Octal Divide bits into groups of 3 1100010110011011 2 1 4 2 6 3 3 8 1. 2. 3. 1 100 010 110 011 011 2 Octal to Binary 1 4 2 6 3 3 8 001 100 010 110 011 011 2

13. Binary01.ppt Hex to Octal to Decimal Break the hex or octal or decimal number into binary 1 0 1 1 1 0 0 0 1 0 1 1 2048 512 256 128 8 2 1 Decimal: add the weights = 2,955 10 Hexadecimal: divide the bits into patterns of 4 = B8B 16 Octal: divide the bits into patterns of 3 = 5613 8