电子科大数字电路课件2-2补码chenyu

Diminished Radix – Complement Representation
[ 基数减1补码表示法（反码）]
The Diminished Radix – Complement of an n-digit number is obtained by subtracting it from r n -1 [ n位数的反码等于从 r n – 1 中减去该数] Example : Table 2-4 ,2-5 P.36 (r-1)’s Complement = r
1、1011100010112= 5613
8=
B8B
16
2、 ( 156 )10 = ( 10011100
)2
3、将0.3910转换为二进制数,要求精度达到10%。 0.3910转换为二进制数 要求精度达到10% 转换为二进制数, 10%。
0.01102
Review of the last lesson
(若约定字长是一个字节，试求－11910的补码表示。)
• +11910＝011101112，as formula(公式): • 2n-D= (2n-1-D)+1 • 28-1： 11111111 subtract(减去)+119; -0 1 1 1 0 1 1 1 • 1 0 0 01 0 0 0 • plus(加)1： + 1 • －11910： 1 0 0 0 1 0 0 12
Binary to Decimal Based on definitions:
00110110 2 = 25 + 2 4 + 2 2 + 21 = 5410
0.00110110 2 = 2 + 2 + 2 + 2 = 0.210937510
−3
−4
−6
−7
0.2109375 × 2 = 54
8
Analog signal
P39
2.5.1 Signed-Magnitude Representation
• a number consists of a magnitude and a symbol indicating whether the magnitude is positive or negative. • MSB as the Sign bit (0 = plus, 1 = minus)
Two’s- Complement ( 二进制补码的取 )
• Example 1. Write the 8-bit two’s-complement representation for the decimal number: -119. (若约定字长是一个字节，试求－11910的补码表示。) • +11910＝011101112，
subtraction produces another number between 1 and r n - 1. what is the result of the subtraction, If D is 0?
2.5.3 Radix-Complement Representation r’s complement= r
2-n
quantized error : 2-n-1 Transmit on data bus with n-bit width
Signals in electric circuit
Digit in decimal system
Digit in binary system
2.5 Representation of Negative Numbers (负数的表示)
2.5.3 Radix-Complement Representation
Advantage
•r
n
–D= [(r
n
-1)-D]+1
This can be accomplished by complementing the individual digits of D,
2.5.4 Two’s – Complement Representation (二进制补码表示法 P37 二进制补码表示法) 二进制补码表示法 1. Two’s- Complement( 二进制补码的求取 )： ： 2. MSB (the sign bit) : 1 =minus; 0=plus Weight of the MSB: -2n-1
*2.5.6 (P38)
there are two representations of zero, positive zero (00 × × × 00) and negative zero (11 × × × 11).
n
– 1-D
2.5.3 Radix-Complement Representation
x = D ⋅ Vs
Analog signal: its measured value changed continually between voltage source and ground. Vs D is a number between 0 and 1;
Analog to Digital
[最高有效位表示符号位（ 0 = 正，1 = 负）] 最高有效位表示符号位（ 最高有效位表示符号位
01111111＝＋ ＝＋127 ＝＋ 00101110＝＋ ＝＋46 ＝＋ 00000000＝＋ ＝＋0 ＝＋ 11111111＝－ ＝－127 ＝－ 10101110＝－ ＝－46 ＝－ 10000000＝－ ＝－0 ＝－
Use one binary number: 1 or 0 ? Divide voltage area into 2 states:
x = D ⋅ Vs
Analog to digital
Mean value:
x = D ⋅ Vs
1 : 3/4
0: 1/4
Quantized step : 1/2 Mean error: 1/4 Maximum error: 1/2
•
2.5.1 Signed-Magnitude Representation [符号 – 数值表示法（原码）]
1. Two possible representations of Zero [零有两种表示（+ 0、 – 0）] 2. An n-bit signed-magnitude integer range is (n位二进制整数表示范围)： – ( 2n-1 – 1) ~ + ( 2n-1 – 1) – The signed-magnitude system has an equal number of positive and negative integers.
• Positional Number Systems
• • • • MSD，LSD，MSB，LSB General Positional-Number-System Conversions A decimal fraction ⇒ A number in Binary radix Binary addition and subtraction
D. (P35)
2.5.3 Radix-Complement Representation
The complement of an n-digit number is obtained by subtracting it from r n .
r’s complement= r
(n (n位数D的基数补码等于从 r D
3. The range of representable numbers is -(2 n-1) through +(2 n-1 -1).
Two’s- Complement ( 二进制补码的求取 )
• Example 1. Write the 8-bit two’s-complement representation for the decimal number: -119.
n
n
-D
中减去该数) )
Example : Table 2-4 P36
2.5.3 Radix-Complement Representation
2.5.3 Radix-Complement Representation r’s complement= r
n
-D
If D is between 1 and rn – 1, this
n
-D
If D is between 1 and rn – 1, this
subtraction produces another number between 1 and r n - 1. what is the result of the subtraction, If D is 0? 0000000…0 (n-bit) (positive) there is only one representation of zero in a radix-complement system.
2.5.2
•
2.5.2 Complement Number Systems (补码数制 补码数制) 补码数制 an n-bit number D D = dn–1dn–2· · ·d1d0 .
The radix point is on the right and so the number is an integer. If an operation produces a result that requires more than n digits, we throw away the extra highorder digit(s). If a number D is complemented twice, the result is