Binary Number System And Conversion

1. Binary Number System And Conversion

2. Bridging the Digital Divide Decimal-to-Binary Conversion 010 00100 10101 1101 10010 16 16 63 00101101 0101011 010 63 23 1101 23 1101 010 1101 10010 935 935 00100 721 721 010 00101 534 534 00101101 Binary-to-Decimal Conversion 011011 935 935 275 275 1101 011011 00100 234 234 00101101 137 011011 137 0101011 0101011 145 145 1101 10010 10010 10101 001011 011011 00101101 00100

3. Decimal ‒to‒ Binary Conversion Step 1: Divide the Decimal Number by 2. STEP 2: If the quotation is zero, the conversion is complete; else repeat step (a) using the quotation as the Decimal Number. The new remainder is the next most significant bit of the Binary Number. .

4. Example: Convert the decimal number 2610 into its binary equivalent.

5. Binary ‒to‒ Decimal Process STEP 1: Multiply each bit of the Binary Number by it corresponding bit-weighting factor (i.e. Bit-0→20=1; Bit-1→21=2; Bit-2→22=4; etc). STEP 2: Sum up all the products in step (a) to get the Decimal Number.

6. Example: Convert the binary number 01102 into its decimal equivalent.

7. OCTAL TO DECIMAL It has a base of 8 and it uses the digits 0,1,2,3,4,5,6,7. Example Convert the octal number 3058 into its decimal equivalent:

8. EXAMPLE Convert the octal number 7532.6258 into its decimal equivalent

9. DECIMAL TO OCTAL Procedure to convert decimal number system to octal system is similar to that of conversion from decimal to binary. Example: convert the decimal number 12510 into its octal number.

10. EXAMPLE: Convert the decimal number 0.625 into its octal number.

11. BINARY NUMBER TO OCTAL NUMBER Octal system has a base of 8, so for binary to octal conversion, make a groups of three digits from right to left in the integer part of the binary number and from left to right in the binary fractional part. Example: Convert the binary number 101111100 into octal number

12. EXAMPLE Convert the binary number .001110 to octal number

13. OCTAL NUMBER TO BINARY NUMBER Replace each octal digit by a set of three binary digits and group these together. Example: Convert the octal number 305 into binary equivalent.

14. EXAMPLE Convert the octal number 225.34 into binary equivalent.

15. HEXADECIMAL NUMBER TO DECIMAL NUMBER Hexadecimal system has a base of 16 and uses the digits 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. Since its base is 24 = 16, therefore, every hexadecimal digit can be represented as a group of 4 bits.

16. EXAMPLE Convert hexadecimal number 3FA.8 into decimal equivalent.

17. DECIMAL NUMBER SYSTEM TO HEXADECIMAL NUMBER SYSTEM Procedure of conversion of decimal into hexadecimal is similar to that of the conversion of decimal into octal (or binary). Here base is 16 in place of 8 (or 2).

18. EXAMPLE Convert decimal number 7547 into hexadecimal number.

19. HEXADECIMAL NUMBER INTO BINARY NUMBER AND VICE VERSA Hexadecimal system has a base of 24 =16, so in binary to hexadecimal conversion, make groups of 4 digits from right to left in the integer part of the binary number and from left to right in the binary fraction part. Similarly from hexadecimal to binary conversion, replace each digit by a set of four binary digits.

20. EXAMPLE Convert binary number 110101.1101 into their hexadecimal equivalents.

21. EXAMPLE Convert hexadecimal number 1BCE into binary number

22. HEXADECIMAL NUMBER INTO OCTAL NUMBER Convert hexadecimal number 4AB into octal number Step 1: The hexadecimal is first converted into its binary equivalent

23. STEP 2: Now the above binary number is divided into the groups of 3 bits to obtain the octal equivalent 010 010 101 011

24. OCTAL NUMBER TO HEXADECIMAL NUMBER STEP 1: Octal number is first converted into its binary equivalent

25. STEP 2: Now the above binary number is converted into the groups of 4 bits to obtain the hexadecimal equivalent

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