- 1. 2 ASCIIUnicode 01 2-21
2. ( 0 ) ( ) ( ) ( IC ) IC 01000001IC 8 0V +5V 0V 0V 0V 0V 0V
+5V8 0 1 0 00 0 0 1 2-3 binary digitbit011 088byteByte28 2562-4 2
3. Kilo210 = 1,024 (103) KB238 KB ByteMega 20 MB2 = 1,048,576
(106)512 MBByte DVD Giga230 = 1,073,741,824 (109) GB4.7 GB Byte240
= Tera(1012) 20 TB TB Byte 1,099,511,627,776 2-5 2-63 4. Coded and
Decoded 2-7 523332255523 = 5 x102 + 2 x 101 +
3Bdndn-1d2d1.r1r2rm-1rmdn x Bn-1 + dn-1 x Bn-2 + + d2 x B1 + d1 x
B0 +r1 x B-1 + r2 x B-2 + + rm-1 x B-(m-1) + rm x B-mB=22-84 5.
2-910110101.11012181.8125 2-105 6. 181101101012 2-110.81250.11012
2-126 7. 0.1 0.1 0.0001100112 2-13 A 4-bit pattern can be
representedby a hexadecimal digit, and vice versa. Bit Pattern Bit
Pattern Hex Digit Hex Digit ------------ ------------ ------------
------------00001000 0 800011001 1 900101010 2 A00111011 3
B01001100 4 C01011101 5 D01101110 6 E01111111 7 F 2-14 7 8. Binary
to hexadecimal andHexadecimal to binary transformation
2-15110110101.1101121B5.D816 2-16 8 9. 2-17__N 2-18 9 10. A 3-bit
pattern can be represented by an octal digit, and vice versa.Bit
Pattern Bit Pattern Oct DigitOct Digit ------------ ------------
------------ ------------ 000 100 0 4 001 101 1 5 010 110 2 6 011
111 3 72-19 Binary to octal and Octal to binary transformation 2-20
10 11. Taxonomy of integers8 = 00001000-811110111 111110002-21
Unsigned integer range: 0 (2N-1) 2-2211 12. Sign-and-magnitude
integersIn sign-and-magnitude representation,the leftmost bit
defines the sign of the number. If it is 0, the number
ispositive.If it is 1, the number is negative. 2-23 Range:
-(2N-1-1) +(2N-1-1) 2-24 12 13. Sign-and-magnitude integersNote:
There are two 0s in sign-and-magnitude representation: positive and
negative.In an 8-bit allocation: +000000000 -010000000 2-25 1 2 n -
1 (overflow)0n 3 0110Range: -(2N-1-1) +(2N-1-1) 2-2613 14.
-4111010110 2-27 0 1 0110 110101101011000101001 00101001 41-41
2-2814 15. Ones complement integers Note:There are two 0s in ones
complement representation: positive and negative.In an 8-bit
allocation: +000000000 -011111111 2-29Ones complement integers
Note: In ones complement representation,the leftmost bit defines
the sign of the number.If it is 0, the number is positive.If it is
1, the number is negative.2-30 15 16. Ones complement integers
Note: Ones complement means reversing all bits.If you ones
complement a positive number,you get the corresponding negative
number.If you ones complement a negative number,you get the
corresponding positive number.If you ones complement a number
twice, youget the original number. 2-31 1 2 n-1 (overflow)0n
-2n-11n-10 3 010110Range: -(2N-1) +(2N-1-1) 2-3216 17. 40-40 ?40
40101000000101000800101000-40 40101000000101000801011011011000
2-33Twos complement integers 0000000000101000 1111111111011000
216-00000000001010000000000000101000Ones complement1111111111010111
10000000000000000 +111111111110110001111111111011000-)
000000000010100011111111110110002-34 17 18. Twos complement
integers Note: In twos complement representation,the leftmost bit
defines the sign of the number.If it is 0, the number is
positive.If it is 1, the number is negative. 2-35-4028-40 2-36 18
19. 0 1 01 0110 110110001010110001010000010100040-40 2-37 2-3819
20. Twos complement integersNote: There is only one 0 in twos
complement:In an 8-bit allocation:000000000 2-39 Twos complement
integersNote: Twos complement can be achieved by reversing allbits
except the rightmost bits up to the first 1(inclusive).If you twos
complement a positive number, you getthe corresponding negative
number.If you twos complement a negative number, you getthe
corresponding positive number.If you twos complement a number
twice, you get theoriginal number. 2-4020 21. Addition in twos
complement Note: Rule of Adding Integers in Twos Complement Add 2
bits and propagate the carryto the next column. If there is a final
carry after the leftmost column addition, discard it. 2-41 2-4221
22. 2-43 2-4422 23. 2-45 2-46 23 24. 2-47n bits + ()(-x) + (-y)-x
2n-x-y 2n-y 2n - x + 2n - y = 2n + (2n - (x+y)) -(x+y)2-4824 25.
(x) + (-y)-y 2n-y 2n+x-y (1) x >= yx-y0; 2n (2) x
