Computer Logical Organization 简明教程

Codes Conversion

有许多方法或技术可以用来将代码从一种格式转换为另一种格式。我们将在本文中演示以下

There are many methods or techniques which can be used to convert code from one format to another. We’ll demonstrate here the following

Binary to BCD Conversion
BCD to Binary Conversion
BCD to Excess-3
Excess-3 to BCD

Binary to BCD Conversion

步骤

Steps

Step 1 — Convert the binary number to decimal.
Step 2 — Convert decimal number to BCD.

示例 − 将 (11101)2 转换为 BCD。

Example − convert (11101)2 to BCD.

Step 1 − Convert to Decimal

二进制数 − 111012

Binary Number − 111012

计算十进制当量 −

Calculating Decimal Equivalent −

Step

Binary Number

Decimal Number

Step 1

111012

1 × 24) + (1 × 23) + (1 × 22) + (0 × 21) + (1 × 2010

Step 2

111012

(16 + 8 + 4 + 0 + 1)10

Step 3

111012

2910

二进制数 − 111012 = 十进制数 − 2910

Binary Number − 111012 = Decimal Number − 2910

Step 2 − Convert to BCD

十进制数 − 2910

Decimal Number − 2910

计算 BCD 等价物。将每个数字转换为四位二进制数字等价物。

Calculating BCD Equivalent. Convert each digit into groups of four binary digits equivalent.

Step

Decimal Number

Conversion

Step 1

2910

00102 10012

Step 2

2910

00101001BCD

结果

Result

(11101)2 =  (00101001)BCD

BCD to Binary Conversion

步骤

Steps

Step 1 — Convert the BCD number to decimal.
Step 2 — Convert decimal to binary.

示例 − 将 (00101001)BCD 转换为二进制。

Example − convert (00101001)BCD to Binary.

Step 1 - Convert to BCD

BCD 数 − (00101001)BCD

BCD Number − (00101001)BCD

计算十进制等价物。将每四位数字转换为一组，并为每一组获取十进制等价物。

Calculating Decimal Equivalent. Convert each four digit into a group and get decimal equivalent for each group.

Step

BCD Number

Conversion

Step 1

(00101001)BCD

00102 10012

Step 2

(00101001)BCD

210 910

Step 3

(00101001)BCD

2910

BCD 数 − (00101001)BCD = 十进制数 − 2910

BCD Number − (00101001)BCD = Decimal Number − 2910

Step 2 - Convert to Binary

用于十进制到二进制转换的长除法方法。

Used long division method for decimal to binary conversion.

十进制数 − 2910

Decimal Number − 2910

计算二进制等价——

Calculating Binary Equivalent −

Step	Operation	Result	Remainder
Step 1	29 / 2	14	1
Step 2	14 / 2	7	0
Step 3	7 / 2	3	1
Step 4	3 / 2	1	1
Step 5	1 / 2	0	1

如步骤 2 和 4 中所述，余数必须按相反的顺序排列，以便第一个余数成为最低有效位数 (LSD)，最后一个余数成为最高有效位数 (MSD)。

As mentioned in Steps 2 and 4, the remainders have to be arranged in the reverse order so that the first remainder becomes the least significant digit (LSD) and the last remainder becomes the most significant digit (MSD).

十进制数 − 2910 = 二进制数 − 111012

Decimal Number − 2910 = Binary Number − 111012

结果

Result

(00101001)BCD = (11101)2

BCD to Excess-3

步骤

Steps

Step 1 — Convert BCD to decimal.
Step 2 — Add (3)10 to this decimal number.
Step 3 — Convert into binary to get excess-3 code.

示例 − 将 (0110)BCD 转换为超额 3。

Example − convert (0110)BCD to Excess-3.

Step 1 − Convert to decimal

(0110)BCD = 610

Step 2 − Add 3 to decimal

(6)10 + (3)10 = (9)10

Step 3 − Convert to Excess-3

(9)10 = (1001)2

结果

Result

(0110)BCD = (1001)XS-3

Excess-3 to BCD Conversion

步骤

Steps

Step 1 — Subtract (0011)2 from each 4 bit of excess-3 digit to obtain the corresponding BCD code.

示例 - 将 (10011010)XS-3 转换为 BCD。

Example − convert (10011010)XS-3 to BCD.

Given XS-3 number  = 1 0 0 1 1 0 1 0
Subtract (0011)2   = 1 0 0 1 0 1 1 1
                    --------------------
               BCD = 0 1 1 0   0 1 1 1

结果

Result

(10011010)XS-3 = (01100111)BCD