Chapter 3 Number Systems and Boolean Algebra 3.1.1 Digits Before numbers are converted from one number base to another the digits of a number system must be understood. Early in our education. we learned that a decimal or base 10 number was constructed with 10 digits: 0 through 9. The first digit in any numbering system is always a zero. For example, a base 8(octal) number contains 8 digits: 0 through 7; a base 2(binary) number contains 2 digits: 0 and 1 将数从一种数制向另一种数制转换之前,必须了解数的计数系统。在早期 教育中,我们已学习了十进制数,或以10为基的数,它由10个数字组成:0 到9。任何计数制的第一个数字总是零,这种规则适用于任何其他数制。例 如,以8为基的数(八进制包含8个数字:0到7,而以2为基的数(二进制)包 含2个数字:0和l 《什第机专出美语 3-6
Chapter 3 Number Systems and Boolean Algebra 计算机专业英语 3-6 Before numbers are converted from one number base to another, the digits of a number system must be understood. Early in our education, we learned that a decimal, or base 10, number was constructed with 10 digits: 0 through 9. The first digit in any numbering system is always a zero. For example, a base 8 (octal) number contains 8 digits: 0 through 7; a base 2 (binary) number contains 2 digits: 0 and 1. 3.1.1 Digits 将数从—种数制向另一种数制转换之前，必须了解数的计数系统。在早期 教育中，我们已学习了十进制数，或以10为基的数，它由10个数字组成：0 到9。任何计数制的第一个数字总是零，这种规则适用于任何其他数制。例 如，以8为基的数(八进制)包含8个数字：0到7，而以2为基的数(二进制)包 含2个数字：0和l
Chapter 3 Number Systems and Boolean Algebra 3.1.1 Digits If the base of a number exceeds 10. the additional digits use the letters of the alphabet, beginning with an A, For example, a base 12 number contains 12 digits: 0 through 9, followed by A for 10 and B for 11, Note that a base 10 number does not contain a 10 digit, just as a base 8 number does net contain an 8 digit. The most common numbering systems used with computers are decimal, binary, and hexadecimal(base 16). Many years ago octal numbers were popular. Each system is described and used in this section of the chapter. 如果基数大于10,其余数字用从A开始的字母表示,例如,以12为基的数包含12个数 字,0到9,之后用A代表10,B代表11。注意,以10为基的数不包含数字10,如同以8 为基的数不包括数字8一样。计算机中最通用的计数制是十进制、二进制、八进制和 十六进制(基为16)。每种计数制都将在本节中进行说明和应用。 《什第机专出美语
Chapter 3 Number Systems and Boolean Algebra 计算机专业英语 3-7 If the base of a number exceeds 10, the additional digits use the letters of the alphabet, beginning with an A, For example, a base 12 number contains 12 digits: 0 through 9, followed by A for 10 and B for 11, Note that a base 10 number does not contain a 10 digit, just as a base 8 number does net contain an 8 digit. The most common numbering systems used with computers are decimal, binary, and hexadecimal (base 16). (Many years ago octal numbers were popular.) Each system is described and used in this section of the chapter. 3.1.1 Digits 如果基数大于10，其余数字用从A开始的字母表示，例如，以12为基的数包含12个数 字，0到9，之后用A代表10，B代表11。注意，以10为基的数不包含数字10，如同以8 为基的数不包括数字8一样。计算机中最通用的计数制是十进制、二进制、八进制和 十六进制(基为16)。每种计数制都将在本节中进行说明和应用
Chapter 3 Number Systems and Boolean Algebra 3.1.2 Positional notation Once the digits of a number system are understood, larger numbers are constructed by using positional notation. In grade school, we learned that the position to the left of the units position was the tens position, the position to the left of the tens position was the hundreds position, and so forth.(An example is the decimal number 132 This number has 1 hundred. 3 tens and 2 units. What probably was not learned was the exponential value of each position: The units position has a weight of 100 or 1; the tens position has weight of 101, or 10 and the hundreds position has a weight of 102, or 100. 旦我们理解了计数制的数字后,就可用位计数法构造更大的数值。在小学时我 们都学过个位的左边一位是十位,十位左边一位是百位,以此类推(例如十进制数 132,这个数字有一个百,三个十和两个一)。或许我们没有学过每个位的指数值 个位的权为00,即1;十位的权为101或10;而百位的权为102或100 N什第机专出关语 3-8
Chapter 3 Number Systems and Boolean Algebra 计算机专业英语 3-8 Once the digits of a number system are understood, larger numbers are constructed by using positional notation. In grade school, we learned that the position to the left of the units position was the tens position, the position to the left of the tens position was the hundreds position, and so forth. (An example is the decimal number 132: This number has 1 hundred, 3 tens, and 2 units.) What probably was not learned was the exponential value of each position: The units position has a weight of 100 or 1; the tens position has weight of 101, or 10; and the hundreds position has a weight of 102, or 100. 3.1.2 Positional Notation 一旦我们理解了计数制的数字后，就可用位计数法构造更大的数值。在小学时我 们都学过个位的左边一位是十位，十位左边一位是百位，以此类推(例如十进制数 132,这个数字有—个百，三个十和两个一)。或许我们没有学过每个位的指数值： 个位的权为l00，即1；十位的权为101或10；而百位的权为102或l00
Chapter 3 Number Systems and Boolean Algebra 3.1.2 Positional notation The exponential powers of the positions are critical for understanding numbers in other numbering systems. The position to the left of the radix (number base) point, called a decimal point only in the decimal system, is always the units position in any number system. For example, the position to the left of the binary point is always 20 or 1; the position to the left of the octal point is 80 or 1. In any case, any number raised to its zero power is always 1, or the units position 位的指数幂在理解其他计数制中的数时是个关键。基数小数 点,在十进制中称为十进制小数点,其左边的位在任何数制 中都是个位。例如,二进制小数点左边的位是20或1。而八进 制小数点左边的位是80或1。在任何情况下,任何数的零次幂 总是1,或个单位。 计算机专业英语 39
Chapter 3 Number Systems and Boolean Algebra 计算机专业英语 3-9 The exponential powers of the positions are critical for understanding numbers in other numbering systems. The position to the left of the radix (number base) point, called a decimal point only in the decimal system, is always the units position in any number system. For example, the position to the left of the binary point is always 20 or 1; the position to the left of the octal point is 80 or 1. In any case, any number raised to its zero power is always 1, or the units position. 3.1.2 Positional Notation 位的指数幂在理解其他计数制中的数时是个关键。基数小数 点，在十进制中称为十进制小数点，其左边的位在任何数制 中都是个位。例如，二进制小数点左边的位是20或1。而八进 制小数点左边的位是80或1。在任何情况下，任何数的零次幂 总是1，或1个单位
Chapter 3 Number Systems and Boolean Algebra 3.1.2 Positional notation The position to the left of the units position is always the number base raised to the first power, in a decimal system, this is 101, or 10. In a binary system, it is 21, or 2; and in an octal system it is 81, or 8. Therefore, an 1l decimal has a different value from an 11 binary. The ll decimal is composed of I ten plus I unit and has a value of ll units; while the binary number ll is composed of I two plus 1 unit, for a value of 3 decimal units. The 1l octal has a value of g units 个位左边的位总是基数的1次幂,在十进制系统中是101,或 10;在二进制中是21,或2;而在八进制中是81,或8。因此 十进制的11与二进制的11具有不同的数值。十进制11表示一 个10加上一个1,其值为11;二进制1表示个2加上一个1, 其值为3;八进制1的值为9 计算机专业英语 3-10
Chapter 3 Number Systems and Boolean Algebra 计算机专业英语 3-10 The position to the left of the units position is always the number base raised to the first power; in a decimal system, this is l01, or l0. In a binary system, it is 21, or 2; and in an octal system it is 81, or 8. Therefore, an 11 decimal has a different value from an 11 binary. The 1l decimal is composed of 1 ten plus 1 unit and has a value of 11 units; while the binary number 11 is composed of 1 two plus 1 unit, for a value of 3 decimal units. The 11 octal has a value of 9 units. 3.1.2 Positional Notation 个位左边的位总是基数的1次幂，在十进制系统中是101，或 10；在二进制中是21，或2；而在八进制中是81，或8。因此， 十进制的11与二进制的11具有不同的数值。十进制11表示— 个10加上一个1，其值为11；二进制11表示—个2加上—个1， 其值为3；八进制11的值为9