17 shortcut method for hexadecimal to binary

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Unformatted text preview: 4+0+1 = 1310 = D16 00112 = 0 x 23 + 0 x 22 + 1 x 21 + 1 x 2° =0+0+2+1 = 316 Hence, 110100112 = D3,6 Compare the result with the result of Example 3.17. Shortcut Method for Hexadecimal to Binary Conversion The following steps are used in this method: Step 1: Convert the decimal equivalent of each hexadecimal digit to 4 binary digits. Step 2: Combine all the resulting binary groups (of 4 digits each) into a single binary number. Example 3.24. 2AB16 = ?2 Solution: Step 1: Convert the decimal equivalent of each hexadecimal digit to 4 binary digits. 216 = 210 = 00102 A16=10I0 =10102 B16=ll10 =l0ll2 Step 2: Combine the binary groups. 2AB16 = 0010/2 1010/A 1011/B Hence, 2AB16 = 0010101010112 Figure 3.2 summarizes the relationship between the decimal, binary, hexadecimal, and octal number systems. Note that the maximum value for a single digit of octal (7) is equal to the maximum value of three digits of binary. The value range of one digit of octal duplicates the value range of three digits of binary. If octal digits are substituted for binary digits, the substitution is on a one-to-three basis. Thus, computers that print octal numbers instead of binary, while taking memory dump, save one-third of the printing space and time. Decimal Hexadecimal Binary Octal 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 7 8 9 A B C D E F 10 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 Mi 10000 0 1 2 3 4 5 6 7 10 Figure 3.2. Relationship among Decimal, Binary, Hexadecimal and Octal number systems. Similarly, note that the maximum value of one digit in hexadecimal is equal to the maximum value of four digits in binary. Thus, the value range of one digit of hexadecimal is equivalent to the value range of four digits of binary. Therefore, hexadecimal shortcut notation is a one-to-four reduction in the space and time required for memory dump. FRACTIONAL NUMBERS In binary number system, fractional numbers are formed in the same general way as in the decimal number system. For example, in the decimal number s...
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