ch03

Solution
Divide the bit pattern into 4-bit groups (from the right). In this case, add two extra 0s at the left to make the number of bits divisible by 4. So you have 000011100010, which is translated to x0E2.
Example 5
Show the octal equivalent of the bit pattern 1100010.
Solution
Divide the bit pattern into 3-bit groups (from the right). In this case, add two extra 0s at the left to make the number of bits divisible by 3. So you have 001100010, which is translated to 1428.
Table 2.2 Hexadecimal digits
Bit Hex Bit Pattern Digit Pattern ------------ ------------ -----------0000 0 1000 0001 1 1001 0010 2 1010 0011 3 1011 0100 4 1100 0101 5 1101 0110 6 1110 0111 7 1111
3.5 INTEGER REPRESENTATION
Figure 3-5
Range of integers
negative integer
positive integer
Figure 3-6
Taxonomy of integers
Unsigned Integers Format
Most computers define a constant called the maximum unsigned integer. Ranger: 0~ (2N-1)
Figure 2-11
Binary to octal and octal to binary transformation
Example 4
Show the octal equivalent of the bit pattern 101110010.
Solution
Each group of 3 bits is translated to one octal digit. The equivalent is 0562, o562, or 5628.
243=2×102+4 × 101+3 × 100
position value:weight
Figure 3-2
Binary s+1 ×26+1 × 25 + 1×24+1 ×21+1 × 20
3.2 CONVERSION
Figure 3-3
Binary to decimal conversion
Chapter 3
Number Representation
OBJECTIVES
After reading this chapter, the reader should be able to : Convert a number from decimal、 hexadecimal、 octal to binary notation and vice versa.
Understand how floating numbers are stored inside a computer using the exponent （幂，指数）and the mantissa（尾数）.
Contents
3.1 Decimal and Binary
3.2 Conversion
Example 4
Store 258 in a 16-bit memory location.
Solution
First change the number to binary 100000010. Add seven 0s to make a total of N (16) bits, 0000000100000010. The number is stored in the memory location.
0 1 2 4 8 17 35 Dec.
Binary 1 0 0 0 1 1
Figure 3-4
Decimal to binary conversion
3.3 HEXADECIMAL NOTATION
Note:
A 4-bit pattern can be represented by a hexadecimal digit, and vice versa.
Decimal
------------------------------------16 + 0 + 0 + 2 + 1 19
Convert the binary number 1001.101 to decimal. Solution
(1001.101)2 =1×23+0×22+0×21+1×20+1×2-1 +0×2-2+1×2-3 =8+1+0.5+0.125 =(9.625)10
Solution
1100 0011. 1010 1000 C 3. A 8 (11000011.10101)2=(C3.A8)16
Example ?
What is the bit pattern for （8B.C4)16?
Solution
8
B. C 4 1000 1011. 1100 0100
(8B.C4)16 ＝(10001011.110001)2
Hex Digit -----------8 9 A B C D E F
Figure 2-10
Binary to hexadecimal and hexadecimal to binary transformation
Example 1
Show the hexadecimal equivalent of the bit pattern 1100 1110 0010.
3.4 OCTAL NOTATION
Note:
A 3-bit pattern can be represented by an octal digit, and vice versa.
Table 3.3 Octal digits
Bit Oct Bit Oct Pattern Digit Pattern Digit ----------- ----------- ----------- ----------000 0 100 4 001 1 101 5 010 2 110 6 011 3 111 7
Example 3
What is the bit pattern for x24C?
Solution
Write each hexadecimal digit as its equivalent bit pattern to get 001001001100.
Example ?
Show the hexadecimal equivalent of the bit pattern （11000011.10101)2 .
Example 6
What is the bit pattern for 248?
Solution
Write each octal digit as its equivalent bit pattern to get 010100.
Example ?
Show the hexadecimal equivalent of the bit pattern (11110100.1110111)2 .
Example 2 Convert the decimal number 35 to binary. Solution
Write out the number at the right corner. Divide the number continuously by 2 and write the quotient and the remainder. The quotients move to the left, and the remainder is recorded under each quotient. Stop when the quotient is zero.
3.3 Hexadecimal
3.4 Octal
3.5 Integer representation 3.6 Excess System 3.7 Floating-Point Representation
3.1
DECIMAL AND BINARY
Figure 3-1
Decimal system
basis
Understand the different representations of an integer inside a computer: unsigned, sign-and-magnitude, one’s complement, and two’s complement.
Understand the Excess system that is used to store the exponential part of a floating-point number.
Solution
Each group of 4 bits is translated to one hexadecimal digit. The equivalent is xCE2.