Trung tâm đào tạo thiết kế vi mạch Semicon


  • ĐĂNG KÝ TÀI KHOẢN ĐỂ TRUY CẬP NHIỀU TÀI LIỆU HƠN!
  • Đăng ký
    *
    *
    *
    *
    *
    Fields marked with an asterisk (*) are required.
semi1_solvingproblems.jpg

Digital Combinational Logic Part-IV

Email In PDF.

Encoders
An encoder is a combinational circuit that performs the inverse operation of a decoder. If a device output code has fewer bits than the input code has, the device is usually called an encoder. e.g. 2n-to-n, priority encoders.

The simplest encoder is a 2n-to-n binary encoder, where it has only one of 2n inputs = 1 and the output is the n-bit binary number corresponding to the active input

 

Example - Octal-to-Binary Encoder
Octal-to-Binary take 8 inputs and provides 3 outputs, thus doing the opposite of what the 3-to-8 decoder does. At any one time, only one input line has a value of 1. The figure below shows the truth table of an Octal-to-binary encoder.

Truth Table

I0

I1

I2

I3

I4

I5

I6

I7

Y2

Y1

Y0

1

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

1

0

0

1

0

0

0

0

0

0

1

0

0

0

0

1

0

0

0

0

0

1

1

0

0

0

0

1

0

0

0

1

0

0

0

0

0

0

0

1

0

0

1

0

1

0

0

0

0

0

0

1

0

1

1

0

0

0

0

0

0

0

0

1

1

1

1

For an 8-to-3 binary encoder with inputs I0-I7 the logic expressions of the outputs Y0-Y2 are:

Y0 = I1 + I3 + I5 + I7

Y1= I2 + I3 + I6 + I7

Y2 = I4 + I5 + I6 +I7
Based on the above equations, we can draw the circuit as shown below
Circuit

 

Example - Decimal-to-Binary Encoder
Decimal-to-Binary take 10 inputs and provides 4 outputs, thus doing the opposite of what the 4-to-10 decoder does. At any one time, only one input line has a value of 1. The figure below shows the truth table of a Decimal-to-binary encoder.
Truth Table

I0

I1

I2

I3

I4

I5

I6

I7

I8

I9

Y3

Y2

Y1

Y0

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

0

0

0

0

1

0

0

1

0

0

0

0

0

0

0

0

0

1

0

0

0

0

1

0

0

0

0

0

0

0

0

1

1

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

0

0

0

0

1

0

0

0

0

0

1

0

1

0

0

0

0

0

0

1

0

0

0

0

1

1

0

0

0

0

0

0

0

0

1

0

0

0

1

1

1

0

0

0

0

0

0

0

0

1

0

1

0

0

0

0

0

0

0

0

0

0

0

0

1

1

0

0

1

From the above truth table , we can derive the functions Y3, Y2, Y1 and Y0 as given belo.

Y3 = I8 + I9

Y2 = I4 + I5 + I6 + I7

Y1 = I2 + I3 + I6 + I7

Y0 = I1 + I3 + I5 + I7 + I9

Priority Encoder

If we look carefully at the Encoder circuits that we got, we see the following limitations. If more then two inputs are active simultaneously, the output is unpredictable or rather it is not what we expect it to be.

This ambiguity is resolved if priority is established so that only one input is encoded, no matter how many inputs are active at a given point of time.

The priority encoder includes a priority function. The operation of the priority encoder is such that if two or more inputs are active at the same time, the input having the highest priority will take precedence.

Example - 4to3 Priority Encoder

The truth table of a 4-input priority encoder is as shown below. The input D3 has the highest priority, D2 has next highest priority, D0 has the lowest priority. This means output Y2 and Y1 are 0 only when none of the inputs D1, D2, D3 are high and only D0 is high.

A 4 to 3 encoder consists of four inputs and three outputs, truth table and symbols of which is shown below.

Truth Table

D3

D2

D1

D0

Y2

Y1

Y0

 

0

0

0

0

0

0

0

 

0

0

0

1

0

0

1

 

0

0

1

x

0

1

0

 

0

1

x

x

0

1

1

 

1

x

x

x

1

0

0

 

Now that we have the truth table, we can draw the Kmaps as shown below.

Kmaps

 

.

From the Kmap we can draw the circuit as shown below. For Y2, we connect directly to D3.

 

We can apply the same logic to get higher order priority encoders.

 Bạn Có Đam Mê Với Vi Mạch hay Nhúng      -     Bạn Muốn Trau Dồi Thêm Kĩ Năng

Mong Muốn Có Thêm Cơ Hội Trong Công Việc

Và Trở Thành Một Người Có Giá Trị Hơn

Bạn Chưa Biết Phương Thức Nào Nhanh Chóng Để Đạt Được Chúng

Hãy Để Chúng Tôi Hỗ Trợ Cho Bạn. SEMICON  

Lần cập nhật cuối ( Thứ ba, 29 Tháng 3 2022 00:11 )