Vector indexing, bit order and signedness

An index is a name; declaration direction determines its meaning

In logic [7:0] a;, a[7] is the leftmost position. In logic [0:7] b;, b[0] is leftmost. Assigning 8'h96 to both gives the same left-to-right pattern, 10010110, but different indices for each bit. The assumption “bit 0 is always the LSB^{iLSB The bit with the lowest place value. Check both the notation direction and the indexing rules.}” is valid only after checking declaration direction.

In practice, consistent direction throughout an interface makes review easier. Also specify waveform display order and bit-array order in files. This course's input JSON arrays are LSB first, while RTL vector displays are generally read MSB^{iMSB The bit with the highest place value. Its index depends on the vector's declaration direction, so do not assume it always has the largest index.} first.

Verify shift direction from the actual connections

In q <= {q[1:0], din};, next q[2] is old q[1], next q[1] is old q[0], and next q[0] is din.

Which index receives which signal is a more precise specification than whether a diagram points left.

The arrows below show the storage positions a bit traverses. Every register^{iRegister A circuit that stores multiple bits of state. The synchronous registers in this course store their specified inputs at a clock edge. Learn more} reads old values at the same edge. They do not imply that din passes all the way to q2 in one edge.

Arithmetic and logical shifts

>> is a logical right shift that fills the vacant left, most significant positions with zeros. >>> can implement an arithmetic right shift with sign extension when its left operand is signed. Identical bits can produce different results depending on the operand's signed declaration.

logic signed [7:0] x;
logic [7:0] logical_right, arithmetic_right;
assign logical_right = x >> 1;
assign arithmetic_right = x >>> 1;

For x=8'b11111000 (-8), the results are 01111100 and 11111100 respectively. Arithmetic right shifting a negative number does not always follow the same rounding rule as signed integer division; check this separately in numerical algorithms.