1.3.2 BINARY ARITHMETIC

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)

Note:  The rules of binary addition (without carries) are the same as the truths of the XOR gate.

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)

 

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)

 

Note:  The rules of binary multiplication are the same as the truths of the AND gate.

 

Binary Division

Binary division is the repeated process of subtraction, just as in decimal division.

For example,

00101010 ÷ 00000110 = 00000111									1	1	1	=	7(base 10)
		1  1  0	)	0	0	1	10	1	0	1	0	=	42(base 10)
						-	1	1	0			=	6(base 10)
								1					borrows
							1	0	10	1
							-	1	1	0
									1	1	0
								-	1	1	0
											0