Binary Arithmetic

Rules of 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)