Binary Operation (Digital Electronics)

Feb 8 • Engineering Notes • 2596 Views • 2 Comments on Binary Operation (Digital Electronics)

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Binary Numbers

In mathematics and computer science , the Binary numeral system, or base-2 numeral system, represents numeric values using two symbols: 0 and 1. More specifically, the usual base2 system is a positional system with a radix of 2. Numbers represented in this system are commonly called binary numbers. Because of its straightforward implementation in digital elecronic circuitry using logic gates, the Binary system is used internally by almost all modern computer and computer based devices such as mobile phones.

Binary Operations
BINARY ADDITION
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0, and carry 1 to the next more significant bit
For example,

00011010 + 00001100 = 00100110 1 1 carries
0 0 0 1 1 0 1 0 = 26(base 10)
+ 0 0 0 0 1 1 0 0 = 12(base 10)
= 0 0 1 0 0 1 1 0 = 38(base 10)

00010011 + 00111110 = 01010001 1 1 1 1 1 carries
0 0 0 1 0 0 1 1 = 19(base 10)
+ 0 0 1 1 1 1 1 0 = 62(base 10)
=0 1 0 1 0 0 0 1 = 81(base 10)
Note: The rules of binary addition (without carries) are the same as the truths of the XOR gate.

Rules of Binary Subtraction

0 – 0 = 0
0 – 1 = 1, and borrow 1 from the next more significant bit
1 – 0 = 1
1 – 1 = 0
For example,

00100101 – 00010001 = 00010100 0 borrows
0 0 1 10 0 1 0 1 = 37(base 10)
– 0 0 0 1 0 0 0 1 = 17(base 10)
= 0 0 0 1 0 1 0 0 = 20(base 10)

00110011 – 00010110 = 00011101 0 10 1 borrows
0 0 1 1 0 10 1 1 = 51(base 10)
– 0 0 0 1 0 1 1 0 = 22(base 10)
= 0 0 0 1 1 1 0 1 = 29(base 10)

Rules of Binary Multiplication

0 x 0 = 0
0 x 1 = 0
1 x 0 = 0
1 x 1 = 1, and no carry or borrow bits
For example,

00101001 × 00000110 = 11110110 0 0 1 0 1 0 0 1 = 41(base 10)
× 0 0 0 0 0 1 1 0= 6(base 10)
0 0 0 0 0 0 0 0
0 0 1 0 1 0 0 1
0 0 1 0 1 0 0 1

0 0 1 1 1 1 0 1 1 0 = 246(base 10)

00010111 × 00000011 = 01000101 0 0 0 1 0 1 1 1 = 23(base 10)
× 0 0 0 0 0 0 1 1 = 3(base 10)
1 1 1 1 1 carries
0 0 0 1 0 1 1 1
0 0 0 1 0 1 1 1

0 0 1 0 0 0 1 0 1 = 69(base 10)
Note: The rules of binary multiplication are the same as the truths of the AND gate.

Another Method: Binary multiplication is the same as repeated binary addition; add the multicand to itself the multiplier number of times.

For example,

00001000 × 00000011 = 00011000 1 carries
0 0 0 0 1 0 0 0 = 8(base 10)
0 0 0 0 1 0 0 0 = 8(base 10)
+ 0 0 0 0 1 0 0 0 = 8(base 10)
0 0 0 1 1 0 0 0 = 24(base 10)

Notes

Binary Number System
System Digits: 0 and 1
Bit (short for binary digit): A single binary digit
LSB (least significant bit): The rightmost bit
MSB (most significant bit): The leftmost bit
Upper Byte (or nybble): The right-hand byte (or nybble) of a pair
Lower Byte (or nybble): The left-hand byte (or nybble) of a pair

Binary Equivalents
1 Nybble (or nibble) = 4 bits
1 Byte = 2 nybbles = 8 bits
1 Kilobyte (KB) = 1024 bytes
1 Megabyte (MB) = 1024 kilobytes = 1,048,576 bytes
1 Gigabyte (GB) = 1024 megabytes = 1,073,741,824 bytes

Question
1.Define binary logic?
Binary logic consists of binary variables and logical operations. The variables are designated by the alphabets such as A, B, C, x, y, z, etc., with each variable having only two distinct values: 1 and 0. There are three basic logic operations: AND, OR, and NOT.

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2 Responses to Binary Operation (Digital Electronics)

  1. million gessese says:

    hard and software communication

  2. million gessese says:

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