& C ONVERSIONS
Spring 2010关于历史的书籍
Addition of one’s complement numbers Binary codes
Readings
Unit 1.2~1.5
Number Systems and Conversions
I RIS H.-R. J IANG
Each digit is multiplied by an appropriate诊所
in the number
parates the positive and negative powers of ba
+7x10-1+8x10-2
Number Systems (2/2)
Examples:
Decimal (ba 10) numbers
953.7810=9x10
Binary (ba 2) numbers
1011.112=1x2
Octal (ba 8) numbers
147.3=1x82+4x8
4
3456789A B C D E F 10
…
Continued until we finally obtain ……………………. e.g., convert 5310Number Systems and Conversions
25322621326232
10
I RIS H.-R. J IANG
Conversion of a Decimal Fraction (1/2)
using multiplication :-3R -3+ ... + a -m R -m = a -1+ F 1F 2
a sufficient number of digits integer fraction
Conversion of a Decimal Fraction (2/2)
Sometimes, the result is a repeating fraction e.g., convert 0.7108
.7x 2(1).4x 2(0).8x 2
x 7
(5).25x 7
(1).75x 7(5).25x 7(1).75
Repeat! .517…… rem. 3 = 63.517
fraction
Binary octal
1001101.010111
Binary hexadecimal
1001101.010111Number Systems and Conversions叠被子英语
Binary Arithmetic --
Addition table: 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1
1 + 1 = 0 (and carry 1 to the next column) e.g., add 1310and 12我最喜欢的一堂语文课作文
<, multiply 1310Number Systems and Conversions
1101 = 13x 1011 = 111101
1101
00001101
10001111 I RIS H.-R. J IANG
Is similar to (easier than) decimal division 10010001 = 14510dividend
1101 = quotient
2009 AMC8
冯㑅⨕㪋A, B, C ⊈D 冣
word表格行高℅A, B, C, D 圦䕂㐶⨕㽸ḓ
Remark: decimal
16
AB + CA DA -
坩ờḋ, 㨢朊㓭坩ờḋ)
Addition of one’s complement numbers
Number Systems and Conversions王牌汽车
I RIS H.-R. J IANG
1)-bit magnitude
Is common for people but awkward for computers
Signed Binary Integers 20中国黄酒
家长说+N
Positive
integers
(all systems)
+0
+1
+2
+3
0000
0001
0010
0011
-0
-
1
-2
-3
