binary addition section 4.5. binary addition example
Post on 11-Jan-2016
229 Views
Preview:
TRANSCRIPT
Binary Addition
Section 4.5
Binary Addition Example
Binary Addition (2)
Derivation of ∑
Question: What primitive best implements ∑? • Inputs: A, B• Outputs: ∑=
B A ∑
0 0 0
1 0 1
0 1 1
1 1 0
Derivation of Carry Out
Question: What primitive best implements Co? • Inputs: A, B• Outputs: Co =A∙B
B A Co
0 0 0
1 0 0
0 1 0
1 1 1
Implementation of a Half-Adder
Limitation of a Half Adder
A half-adder does not account for carry-in.
Truth Table for a Full Adder
carry-in
Karnaugh Map For the Sum Bit
= = =
Karnaugh Map For the Carry-Out Bit
C=𝑥 ′ 𝑦𝑧+𝑥 𝑦 ′ 𝑧+𝑥𝑦=𝑧 (𝑥⊕𝑦 )+𝑥𝑦
Implementation of a Full Adder
𝑆=𝑧 (𝑥⊕ 𝑦 )+𝑥𝑦C=𝑧⊕(𝑥⊕𝑦 )
(carry-in)
Four-Bit Adder
C4 is calculated last because it takes C0 8 gates to reach C4.
Alternative Naming Convention for the Full Adder
𝐺𝑖=𝐴𝑖𝐵 𝑖P i=(𝐴𝑖⊕𝐵𝑖)
C 𝑖+1=𝐺𝑖+𝑃𝑖𝐶𝑖S i=(𝑃𝑖⊕𝐶𝑖)
Hardware Simplificationinput carry
)
2 gate delays for C3!
Four-bit adder with Carry Lookahead
top related