1. Converting Binary to Octal
start
STEP ONE: Take the binary number and from right to left, group all placeholders in triplets. Add leading zeros, if necessary:
010
001
100
101
001

2.
214518 =
STEP TWO: Convert each triplet to its single-digit octal equivalent. (HINT: For each triplet, the octal conversion is the same as converting to a decimal number):
010
001
100
101
001 2 1 4 5 1

3. Converting Octal to Binary
435208 =
STEP ONE: Take each octal digit and convert each digit to a binary triplet. Keep leading zeros: 4 3 5 2
100
011
101
010
000

4. Hexadecimal System
Sometimes, it is necessary to use a numbering system that has more than ten base digits
One such numbering system, hexadecimal, is useful on the Web
Hexadecimal number, a Base-16 numbering system, is used in specifying web colors

5. Hexadecimal Numbering
There are new symbols for the Base-16 equivalents of the Base-10 numbers 10, 11, 12, 14 and 15. Examine:
DEC 1 2 3 4 5 6 7
HEX 8 9 10 11 12 13 14 15 A B C D E F

6. Decimal
Hexadecimal
Octal
Binary
0000 1
0001 2
0010 3
0011 4
0100 5
0101 6
0110 7
0111 8 10
1000 9 11
1001

7. Decimal Octal Binary 10 A 12 1010 11 B 13 1011 C 14 1100 D 15 1101 E
Hexadecimal
Octal
Binary 10 A 12
1010 11 B 13
1011 C 14
1100 D 15
1101 E 16
1110 F 17
1111

8. Convert a hexadecimal number to a binary number,
simply divided the binary number into 4-bit groups
substitute the corresponding four bits in binary for each hexadecimal digit in the number.
For example, convert ABCD to a binary value, The binary equivalent is:
ABCD=

9. Binary to Hex Conversion
Break the binary number into 4-bit groups from the Left to the right.
Convert the 4-bit binary number to its Hex equivalent.
For example, the binary value will be written:
=AFB2

10. Hex to Binary Conversion
Convert the Hex number to its 4-bit binary equivalent.
Combine the 4-bit groups by removing the spaces.
For example, the hex value AFC7 will be written:
AFC7=

11. Hex to Decimal Conversion
To convert from Hex to Decimal,
multiply the value in each position by its hex weight and
add each value. use the expansion form
AFB.2=10* * *16+2*16-1

12. Decimal to Hex Conversion
Repeated Division By 16
Divide the decimal number by 16, and write the remainder on the side as the least significant digit.
This process is continued by dividing the quotient by 16 and writing the remainder until the quotient is 0.
the remainders represent the hex equivalent of the decimal number are written beginning at the least significant digit (right) and each new digit is written to the next more significant digit (the left) of the previous digit.

13. Example convert 196710 to Hex 1967/16 122 15 F 122/16 7 10 AF 7/16 7AF
Division
Quotient
Remainder
Hex Number
1967/16
122 15 F
122/16 7 10 AF
7/16
7AF
Then (1967)10 =(7AF)16

14. Decimal fraction to B, O and H
Product with Base
New farction
integer
0.0625
2X0.0625
0.1250 .0
2X0.125
0.250
.00
2X0.25
0.5
.000
1.0
.0001 =

15. Fraction
Product with Base
New fraction
integer
0.0625
8X0.0625
0.5000 .0
0.5
8X0.5
4. 0
.04
= .048
16X0.0625
1.0000 .1
= .116

16. Convert ( )10 to B,O,H
Division
Quotient
Remainder
Hex Number
1967/8
245 7
245/8 30 3 37
30/8 6
376
3/8
3637
(1967)10= (3537)8
= .048
( )10= ( )8

17. Binary Addition + 1 10
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10

18. Multiply Binary numbers* 1
0 * 0 = 0
0 * 1 = 0
1 * 0 = 0
1 * 1 = 1

19. carry
111101
(carry)

20. Multiply 1011 and 1010 1 0 1 1 × 1 0 1 0 --------------- 0 0 0 0 ×

21. ------------------------------------
Multiply Example