[...]... 1010111 -+ 2 = 87; 4" remainder of 1 I.SB 43 i 2 = f l remainder of 1 +7 21 -+ 2 = 10 remainder 10 -+ 2 = 1 of 1 remainder of 0I 4 5 -+ 2 = 2 remainder of 1 F -l remainder of 0 2 i2 = 1 5 1remainder of 1 1 +2 0 = 1 1 -1 1 MSH 87,,-l III 0 1 01 1 " 1 1, Fig 1-4 Decimal-to-binary conversion Convert the decimal number 0.375 to a binary number Figure 1-51 illustrates one method of performing this task Note... radix of 16 It is referred t o as the h e 16 rtirnibvr sysiern It uscs the symbols 0-9, A, B, C D E, and F as shown in thc hexadecinial coluniri of the table in Fig 1-7 The letter A stands for a count of 10 B for 11, C for 12, D for 13, E for 14, and F for 15 Thc advantage of the hexadecimal system is its usefulness in converting dircctly from a 4-bit binary numbcr Notc in thc shaded section of Fig... 00010100 in 2s complement and binary 14 NUMBERS USED IN DIGITAL ELECTRONICS [CHAP 1 Supplementary Problems 1.31 The number system with a radix of 2 is called the number system 1.32 The number system with a radix of 10 is called the 1.33 The number system with a radix of 8 is called the 1.34 The number system with a radix of 16 is called the 1.35 A binary digit is sometimes shortened and called a(n) 1.36... I 103 t 2 51 -+ 2 25 -+ 2 12 + 2 6t2 3+2 I 1 1 1 01011 1 5 = 51 remainder of 1 = 25 remainder of I = 12 remainder of 1 = 6 remainder of 0 = 3 remainder of 0 = 1 remainder of I + 2 = 0 remainder + Binary of 1 I 1 0 0 I I I + 0.5 x 2 = i.0 0.0 x 2 = 0.0 Fig 2-3 BCD-to-binary conversion Step 2 in Fig 2-3 shows the integer part of the decimal nuniber being translated into binary The 103,o is converted... results in a quotient of 0 with a remainder of 2 The 2 becomes the next digit in the 2SO + 16 = 15 remainder of 10 15 +- 16 = 0 remainder of 15 45 -+ 16 = 2 remainder of 13 250.25 A * 4 16 I r J -+ 16 = 0 remainder of 2 0.25 :< 16 = 4.00 2 451@=2 =F I c 0.00 D,, :K 16 = 0.00 (b) Fractional decimal-to-hexadecimal conversion (a) Decimal-to-hexadecimal conversion Fig 1-9 8 NUMBERS USED IN DIGITAL ELECTRONICS... Chapter 2 Binary Codes 2-1 INTRODUCTION Digital systems process only codes consisting of OS and 1s (binary codes) That is due to the bistable nature of digital electronic circuits The straight binary code was discussed in Chap 1 Several other, special binary codes have evolved over the years to perform specific functions in digital equipment All those codes use OS and Is, but their meanings may vary Several... hexadecimal numbers, because of their compactness, are much easier to write down than the long strings of 1s and OS in binary The hexadecimal system can be thought of as a shorthand method of writing binary numbers Figure 1-1Oc shows the binary number 101010000101being converted to hexadecimal First divide the binary number into 4-bit groups starting at the binary point Each group of four bits is then translated... 2 = 1.00 Fig 1-6 Decimal-to-binary conversion SOLVED PROBLEMS 1.1 The binary number system is the base system and has a radix of Solution: The binary number system is the base 2 system and has a radix of 2 1.2 The term bit means when dealing with binary numbers Solution: Bit means binary digit 1.3 How would you say the number 1001 in ( a ) binary and ( b ) decimal? Solution: The number 1001 is pronounced... binary and decimal Powers of 2 2" 23 72 21 20 Place value 16s 8s 4s 25 Is Binary 1 0 0 1 1 Decimal 16 > I + (U) 2 + + Binary point 1 = 1 9 Binary-to-decimal conversion Powers of 2 25 24 23 22 2' 20 Place value 32s 16s 8s 4s 25 Is Binary 1 0 1 1 1 0 Deci ma I 32 + 8 + 4 + 2 -Binary = 46 ( h ) Binary-to-decimal conversion lOollz == 1910 101 1 1 0 2 = 4610 ( c ) Summary of conversions and use of small... reverse the process and convert the decimal number 45 to its hexadecimal equivalent Figure 1-9a details the familiar repeated divide-by-16 process The decimal number 45 is first divided by 16, resulting in a quotient of 2 with a remainder of 13 The remainder of 13 (D in hexadecimal) becomes the LSD of the hexadecimal number The quotient (2) is transferred to the dividend position and divided by 16 This . Supervisor: Patty Andrews Library of Congress Cataloging-in-Publication Data Tokheim, Roger L. Schaum’s outline of theory and problems of digital prinicples/by. equipment and controls, and office, medical, military, and communications equipment. This expanding use of digital circuits is the result of the development