Binary Arithmetic

Visualize binary number operations step by step. Watch carry chains propagate, two's complement negation unfold, and understand how computers perform arithmetic at the bit level.

Digital Logic FoundationsPrerequisite: Number Systems & Logic Gates

Ready. Press Play or Step to begin.Step 0/0

Binary Addition

Carry:

2^7

2^6

2^5

2^4

2^3

2^2

2^1

2^0

= 5

2^7

2^6

2^5

2^4

2^3

2^2

2^1

2^0

= 3

A:00000101=5(u)5(s)

B:00000011=3(u)3(s)

Active Bit

Carry

Result

Overflow

1.0x

Metrics

Carry Count

Current Bit

Result (unsigned)

Result (signed)

Binary Addition

Binary addition follows the same column-by-column process as decimal addition, but with only two digits (0 and 1). When the sum of a column exceeds 1, a carry is generated to the next column.

Rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (0 carry 1), 1+1+1=11 (1 carry 1)

Carry propagation goes from LSB (rightmost) to MSB (leftmost)

The ripple carry adder processes one bit at a time, cascading carries

Faster adders (carry-lookahead) predict carries to speed up addition