Explanation Given information: A binary number 10010101011.101010011 2 . Calculation: Binary number system uses the number 2 as its base. Therefore, it has 2 symbols: The numbers are 0 and 1. And a hexadecimal number system uses the number 16 as its base, i.e., it has 16 symbols. The hexadecimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. Binary numbers are represented as from hexadecimal number Binary 0000 0001 0010 0011 0100 0101 0110 0111 Decimal 0 1 2 3 4 5 6 7 Hexadecimal 0 1 2 3 4 5 6 7 Binary 1000 1001 1010 1011 1100 1101 1110 1111 Decimal 8 9 10 11 12 13 14 15 Hexadecimal 8 9 A B C D E F Each hexadecimal digit consists of 4 binary digits. For example, hexadecimal number 9 is equal to binary number 1001. For converting integer part of binary number into hexadecimal number, write down the binary number and represent four binary digits from right by its hexadecimal digit from the table. Then combine all the digits together. For converting fractional part of binary number into hexadecimal number, write down the binary number and represent four binary digits from left by its hexadecimal digit from the table. Then combine all the digits together. Finally, hexadecimal number is combination of both integer and fractional part. Hexadecimal digits are equal to the summation of 2 n where n = 0, 1, 2 and 3 (position from right). For example, 9 = 2 3 +2 0 . In this example, 2 1 and 2 2 are not there. So, at position 1 and 2, binary digit is zero, and at position 0 and 3, binary digit is one. Therefore, hexadecimal of binary 1001 is The hexadecimal number is equal to the summation of binary digits d n × 2 n Divide the binary number into block of four digits. If four digits are not there, then add additional zero in binary number. For example, 11 is written as 0011 and .11 is written as .1100. Hexadecimal of binary number 1100100101001011.1001001001 2 is (Starting from right for integer part and starting from left for fractional part) b i n a r y n u m b e r = 0100 1010 1011 . 1010 1001 1000 → s i x h e x a d e c i m a l d i g i t s a r e e x i s t f i r s t h e x a d e c i m a l d i g i t = 0 × 2 3 + 1 × 2 2 + 0 × 2 1 + 0 × 2 0 f i r s t h e x a d e c i m a l d i g i t = 0 × 8 + 1 × 4 + 0 × 2 + 0 × 1 f i r s t h e x a d e c i m a l d i g i t = 0 + 4 + 0 + 0 f i r s t h e x a d e c i m a l d i g i t = 4 sec o n d h e x a d e c i m a l d i g i t = 1 × 2 3 + 0 × 2 2 + 1 × 2 1 + 0 × 2 0 sec o n d h e x a d e c i m a l d i g i t = 1 × 8 + 0 × 4 + 1 × 2 + 0 × 1 sec o n d h e x a d e c i m a l d i g i t = 8 + 0 + 2 + 0 sec o n d h e x a d e c i m a l d i g i

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ISBN: 9780100548169

Author: SMITH

Publisher: YUZU

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Chapter 83, Problem 15A

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To express:

A binary number into a hexadecimal number.

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Ch. 83 - Prob. 1A Ch. 83 - Prob. 2A Ch. 83 - Prob. 3A Ch. 83 - Prob. 4A Ch. 83 - Prob. 5A Ch. 83 - Prob. 6A Ch. 83 - Prob. 7A Ch. 83 - Prob. 8A Ch. 83 - Prob. 9A Ch. 83 - Prob. 10A

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To express: A binary number into a hexadecimal number.

Solution Summary: The author explains how hexadecimal numbers are represented in binary and tional form.