4 Binary addition 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 10 = 0 + carry of 1 into next position= 11 = 1 + carry of 1 into next positionHALF ADDERABSUMCOABSUMCO1SUM =(AB) + (AB)Carry-Out =(AB)
5 1-bit 8 Strings Full Adder with Carry-In and Carry-Out Binary addition1-bit 8 Strings Full Adder with Carry-In and Carry-OutCIABSUMCO1FULL ADDERABSUMCOCISUM =(A B)CI + (A B)CI+Carry-Out =(AB)CI + (A+B)CI
6 1-bit 8 Strings Full Adder with Carry-In and Carry-Out SUMCOCISUM =(A B)CI + (A B)CI+Carry-Out =(AB)CI + (A+B)CI
17 Positive and Negative Numbers MagnitudePositiveNegative123456780001001000110100010101100111-11111110110111001011101010011000
18 2’ S-complement representation summary Positive numbers always have a sign bit of 0, and negative numbers always have a sign bit of 1.Positive numbers are stored in sign-magnitude form.Negative numbers are stored as 2’s complements.Taking the 2’s complement is equivalent to a sign change.
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